Some results related to Schiffer's problem
We consider the following semilinear overdetermined problem on a two dimensional bounded or unbounded domain Omega with analytic boundary partial differential partial derivative Omega having at least one bounded connected component {-Delta u = g(u) in Omega, partial derivative u/partial derivative v...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kawohl, Bernhard - 1952- [verfasserIn] Lucia, Marcello [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Ausgabe: |
Published: 26 January 2021 |
| Schlagwörter: |
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| Anmerkung: |
Last seen: 09.02.2023 |
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| Weitere Ausgabe: |
Erscheint auch als Preprint: Some results related to Schiffer's problem - Oberwolfach-Walke : Mathematisches Forschungsinstitut, 2018 |
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| Übergeordnetes Werk: |
Enthalten in: Journal d'analyse mathématique - Berlin : Springer, 1951, Volume 142(2020), Issue 2, pp. 667-696 |
| Übergeordnetes Werk: |
volume:142 ; year:2020 ; number:2 ; pages:667-696 |
| Links: |
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| DOI / URN: |
10.1007/s11854-020-0146-z |
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| Katalog-ID: |
1833787552 |
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| 245 | 1 | 0 | |a Some results related to Schiffer's problem |
| 250 | |a Published: 26 January 2021 | ||
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| 520 | |a We consider the following semilinear overdetermined problem on a two dimensional bounded or unbounded domain Omega with analytic boundary partial differential partial derivative Omega having at least one bounded connected component {-Delta u = g(u) in Omega, partial derivative u/partial derivative v = 0 and u = c on partial derivative Omega where c is a constant. When g(c) = 0 the constant solution u equivalent to c is the unique solution. For g(c) not equal 0, we show that the boundary is a circle if and only if the problem admits a solution that has a constant third or fourth normal derivative along the boundary. A similar result involving the fifth normal derivative is proved. | ||
| 650 | 4 | |a Boundary-value-problems | |
| 650 | 4 | |a Overdetermined problems | |
| 650 | 4 | |a Pompeiu problem | |
| 650 | 4 | |a Radial symmetry | |
| 700 | 1 | |a Lucia, Marcello |e verfasserin |0 (DE-588)1165083825 |0 (DE-627)1029272301 |0 (DE-576)510238769 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Journal d'analyse mathématique |d Berlin : Springer, 1951 |g Volume 142(2020), Issue 2, pp. 667-696 |h Online-Ressource |w (DE-627)53027728X |w (DE-600)2316542-X |w (DE-576)264951751 |x 1565-8538 |7 nnns |
| 773 | 1 | 8 | |g volume:142 |g year:2020 |g number:2 |g pages:667-696 |
| 776 | 0 | 8 | |i Erscheint auch als |n Preprint |t Some results related to Schiffer's problem |d Oberwolfach-Walke : Mathematisches Forschungsinstitut, 2018 |h 1 Online-Ressource (34 Seiten) |w (DE-627)1655292412 |w (DE-576)510238882 |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s11854-020-0146-z |x Resolving-System |y Full Text at Publisher |z lizenzpflichtig |
| 912 | |a GBV_USEFLAG_U | ||
| 912 | |a GBV_ILN_2088 | ||
| 912 | |a ISIL_DE-Frei3c | ||
| 912 | |a SYSFLAG_1 | ||
| 912 | |a GBV_KXP | ||
| 912 | |a GBV_ILN_11 | ||
| 912 | |a GBV_ILN_20 | ||
| 912 | |a GBV_ILN_22 | ||
| 912 | |a GBV_ILN_23 | ||
| 912 | |a GBV_ILN_24 | ||
| 912 | |a GBV_ILN_31 | ||
| 912 | |a GBV_ILN_32 | ||
| 912 | |a GBV_ILN_39 | ||
| 912 | |a GBV_ILN_40 | ||
| 912 | |a GBV_ILN_60 | ||
| 912 | |a GBV_ILN_62 | ||
| 912 | |a GBV_ILN_63 | ||
| 912 | |a GBV_ILN_65 | ||
| 912 | |a GBV_ILN_69 | ||
| 912 | |a GBV_ILN_70 | ||
| 912 | |a GBV_ILN_73 | ||
| 912 | |a GBV_ILN_74 | ||
| 912 | |a GBV_ILN_90 | ||
| 912 | |a GBV_ILN_95 | ||
| 912 | |a GBV_ILN_100 | ||
| 912 | |a GBV_ILN_105 | ||
| 912 | |a GBV_ILN_110 | ||
| 912 | |a GBV_ILN_120 | ||
| 912 | |a GBV_ILN_138 | ||
| 912 | |a GBV_ILN_150 | ||
| 912 | |a GBV_ILN_151 | ||
| 912 | |a GBV_ILN_152 | ||
| 912 | |a GBV_ILN_161 | ||
| 912 | |a GBV_ILN_170 | ||
| 912 | |a GBV_ILN_171 | ||
| 912 | |a GBV_ILN_187 | ||
| 912 | |a GBV_ILN_213 | ||
| 912 | |a GBV_ILN_224 | ||
| 912 | |a GBV_ILN_230 | ||
| 912 | |a GBV_ILN_250 | ||
| 912 | |a GBV_ILN_281 | ||
| 912 | |a GBV_ILN_285 | ||
| 912 | |a GBV_ILN_293 | ||
| 912 | |a GBV_ILN_370 | ||
| 912 | |a GBV_ILN_602 | ||
| 912 | |a GBV_ILN_636 | ||
| 912 | |a GBV_ILN_702 | ||
| 912 | |a GBV_ILN_2001 | ||
| 912 | |a GBV_ILN_2003 | ||
| 912 | |a GBV_ILN_2004 | ||
| 912 | |a GBV_ILN_2005 | ||
| 912 | |a GBV_ILN_2006 | ||
| 912 | |a GBV_ILN_2007 | ||
| 912 | |a GBV_ILN_2008 | ||
| 912 | |a GBV_ILN_2009 | ||
| 912 | |a GBV_ILN_2010 | ||
| 912 | |a GBV_ILN_2011 | ||
| 912 | |a GBV_ILN_2014 | ||
| 912 | |a GBV_ILN_2015 | ||
| 912 | |a GBV_ILN_2020 | ||
| 912 | |a GBV_ILN_2021 | ||
| 912 | |a GBV_ILN_2025 | ||
| 912 | |a GBV_ILN_2026 | ||
| 912 | |a GBV_ILN_2027 | ||
| 912 | |a GBV_ILN_2031 | ||
| 912 | |a GBV_ILN_2034 | ||
| 912 | |a GBV_ILN_2037 | ||
| 912 | |a GBV_ILN_2038 | ||
| 912 | |a GBV_ILN_2039 | ||
| 912 | |a GBV_ILN_2044 | ||
| 912 | |a GBV_ILN_2048 | ||
| 912 | |a GBV_ILN_2049 | ||
| 912 | |a GBV_ILN_2050 | ||
| 912 | |a GBV_ILN_2055 | ||
| 912 | |a GBV_ILN_2056 | ||
| 912 | |a GBV_ILN_2057 | ||
| 912 | |a GBV_ILN_2059 | ||
| 912 | |a GBV_ILN_2061 | ||
| 912 | |a GBV_ILN_2064 | ||
| 912 | |a GBV_ILN_2065 | ||
| 912 | |a GBV_ILN_2068 | ||
| 912 | |a GBV_ILN_2093 | ||
| 912 | |a GBV_ILN_2106 | ||
| 912 | |a GBV_ILN_2107 | ||
| 912 | |a GBV_ILN_2108 | ||
| 912 | |a GBV_ILN_2110 | ||
| 912 | |a GBV_ILN_2111 | ||
| 912 | |a GBV_ILN_2112 | ||
| 912 | |a GBV_ILN_2113 | ||
| 912 | |a GBV_ILN_2118 | ||
| 912 | |a GBV_ILN_2122 | ||
| 912 | |a GBV_ILN_2129 | ||
| 912 | |a GBV_ILN_2143 | ||
| 912 | |a GBV_ILN_2144 | ||
| 912 | |a GBV_ILN_2147 | ||
| 912 | |a GBV_ILN_2148 | ||
| 912 | |a GBV_ILN_2152 | ||
| 912 | |a GBV_ILN_2153 | ||
| 912 | |a GBV_ILN_2188 | ||
| 912 | |a GBV_ILN_2190 | ||
| 912 | |a GBV_ILN_2232 | ||
| 912 | |a GBV_ILN_2336 | ||
| 912 | |a GBV_ILN_2446 | ||
| 912 | |a GBV_ILN_2470 | ||
| 912 | |a GBV_ILN_2472 | ||
| 912 | |a GBV_ILN_2507 | ||
| 912 | |a GBV_ILN_2522 | ||
| 912 | |a GBV_ILN_2548 | ||
| 912 | |a GBV_ILN_4035 | ||
| 912 | |a GBV_ILN_4037 | ||
| 912 | |a GBV_ILN_4046 | ||
| 912 | |a GBV_ILN_4112 | ||
| 912 | |a GBV_ILN_4125 | ||
| 912 | |a GBV_ILN_4126 | ||
| 912 | |a GBV_ILN_4242 | ||
| 912 | |a GBV_ILN_4246 | ||
| 912 | |a GBV_ILN_4249 | ||
| 912 | |a GBV_ILN_4251 | ||
| 912 | |a GBV_ILN_4305 | ||
| 912 | |a GBV_ILN_4306 | ||
| 912 | |a GBV_ILN_4307 | ||
| 912 | |a GBV_ILN_4313 | ||
| 912 | |a GBV_ILN_4322 | ||
| 912 | |a GBV_ILN_4323 | ||
| 912 | |a GBV_ILN_4324 | ||
| 912 | |a GBV_ILN_4325 | ||
| 912 | |a GBV_ILN_4326 | ||
| 912 | |a GBV_ILN_4328 | ||
| 912 | |a GBV_ILN_4333 | ||
| 912 | |a GBV_ILN_4334 | ||
| 912 | |a GBV_ILN_4335 | ||
| 912 | |a GBV_ILN_4336 | ||
| 912 | |a GBV_ILN_4338 | ||
| 912 | |a GBV_ILN_4393 | ||
| 912 | |a GBV_ILN_4700 | ||
| 951 | |a AR | ||
| 952 | |d 142 |j 2020 |e 2 |h 667-696 |y Volume 142(2020), Issue 2, pp. 667-696 | ||
| 980 | |2 2088 |1 01 |x DE-Frei3c |b 4269364009 |c 00 |f --%%-- |d --%%-- |e --%%-- |j n |k Funding text/Acknowledgements: This research was begun during a "Research in Pairs" stay from May 23 to June 14, 2013 at Mathematisches Forschungsinstitut Oberwolfach. We are grateful to MFO and their staff for the excellent working conditions and hospitality. [...] |y l01 |z 09-02-23 | ||
| 981 | |2 2088 |1 01 |x DE-Frei3c |y Oberwolfach Preprint |r https://doi.org/10.14760/OWP-2018-18 | ||
| 983 | |2 2088 |1 01 |x DE-Frei3c |8 00 |0 (DE-627)1295034905 |a AMS:35 |b Partial differential equations | ||
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2020 |
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2020 |
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10.1007/s11854-020-0146-z doi (DE-627)1833787552 (DE-599)KXP1833787552 DE-627 ger DE-627 rda eng 35J25 msc 35N25 msc 35J61 msc 35P99 msc Kawohl, Bernhard 1952- verfasserin (DE-588)142802883 (DE-627)640131042 (DE-576)161668852 aut Some results related to Schiffer's problem Published: 26 January 2021 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 09.02.2023 We consider the following semilinear overdetermined problem on a two dimensional bounded or unbounded domain Omega with analytic boundary partial differential partial derivative Omega having at least one bounded connected component {-Delta u = g(u) in Omega, partial derivative u/partial derivative v = 0 and u = c on partial derivative Omega where c is a constant. When g(c) = 0 the constant solution u equivalent to c is the unique solution. For g(c) not equal 0, we show that the boundary is a circle if and only if the problem admits a solution that has a constant third or fourth normal derivative along the boundary. A similar result involving the fifth normal derivative is proved. Boundary-value-problems Overdetermined problems Pompeiu problem Radial symmetry Lucia, Marcello verfasserin (DE-588)1165083825 (DE-627)1029272301 (DE-576)510238769 aut Enthalten in Journal d'analyse mathématique Berlin : Springer, 1951 Volume 142(2020), Issue 2, pp. 667-696 Online-Ressource (DE-627)53027728X (DE-600)2316542-X (DE-576)264951751 1565-8538 nnns volume:142 year:2020 number:2 pages:667-696 Erscheint auch als Preprint Some results related to Schiffer's problem Oberwolfach-Walke : Mathematisches Forschungsinstitut, 2018 1 Online-Ressource (34 Seiten) (DE-627)1655292412 (DE-576)510238882 https://doi.org/10.1007/s11854-020-0146-z Resolving-System Full Text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 142 2020 2 667-696 Volume 142(2020), Issue 2, pp. 667-696 2088 01 DE-Frei3c 4269364009 00 --%%-- --%%-- --%%-- n Funding text/Acknowledgements: This research was begun during a "Research in Pairs" stay from May 23 to June 14, 2013 at Mathematisches Forschungsinstitut Oberwolfach. We are grateful to MFO and their staff for the excellent working conditions and hospitality. [...] l01 09-02-23 2088 01 DE-Frei3c Oberwolfach Preprint https://doi.org/10.14760/OWP-2018-18 2088 01 DE-Frei3c 00 (DE-627)1295034905 AMS:35 Partial differential equations |
| spelling |
10.1007/s11854-020-0146-z doi (DE-627)1833787552 (DE-599)KXP1833787552 DE-627 ger DE-627 rda eng 35J25 msc 35N25 msc 35J61 msc 35P99 msc Kawohl, Bernhard 1952- verfasserin (DE-588)142802883 (DE-627)640131042 (DE-576)161668852 aut Some results related to Schiffer's problem Published: 26 January 2021 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 09.02.2023 We consider the following semilinear overdetermined problem on a two dimensional bounded or unbounded domain Omega with analytic boundary partial differential partial derivative Omega having at least one bounded connected component {-Delta u = g(u) in Omega, partial derivative u/partial derivative v = 0 and u = c on partial derivative Omega where c is a constant. When g(c) = 0 the constant solution u equivalent to c is the unique solution. For g(c) not equal 0, we show that the boundary is a circle if and only if the problem admits a solution that has a constant third or fourth normal derivative along the boundary. A similar result involving the fifth normal derivative is proved. Boundary-value-problems Overdetermined problems Pompeiu problem Radial symmetry Lucia, Marcello verfasserin (DE-588)1165083825 (DE-627)1029272301 (DE-576)510238769 aut Enthalten in Journal d'analyse mathématique Berlin : Springer, 1951 Volume 142(2020), Issue 2, pp. 667-696 Online-Ressource (DE-627)53027728X (DE-600)2316542-X (DE-576)264951751 1565-8538 nnns volume:142 year:2020 number:2 pages:667-696 Erscheint auch als Preprint Some results related to Schiffer's problem Oberwolfach-Walke : Mathematisches Forschungsinstitut, 2018 1 Online-Ressource (34 Seiten) (DE-627)1655292412 (DE-576)510238882 https://doi.org/10.1007/s11854-020-0146-z Resolving-System Full Text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 142 2020 2 667-696 Volume 142(2020), Issue 2, pp. 667-696 2088 01 DE-Frei3c 4269364009 00 --%%-- --%%-- --%%-- n Funding text/Acknowledgements: This research was begun during a "Research in Pairs" stay from May 23 to June 14, 2013 at Mathematisches Forschungsinstitut Oberwolfach. We are grateful to MFO and their staff for the excellent working conditions and hospitality. [...] l01 09-02-23 2088 01 DE-Frei3c Oberwolfach Preprint https://doi.org/10.14760/OWP-2018-18 2088 01 DE-Frei3c 00 (DE-627)1295034905 AMS:35 Partial differential equations |
| allfields_unstemmed |
10.1007/s11854-020-0146-z doi (DE-627)1833787552 (DE-599)KXP1833787552 DE-627 ger DE-627 rda eng 35J25 msc 35N25 msc 35J61 msc 35P99 msc Kawohl, Bernhard 1952- verfasserin (DE-588)142802883 (DE-627)640131042 (DE-576)161668852 aut Some results related to Schiffer's problem Published: 26 January 2021 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 09.02.2023 We consider the following semilinear overdetermined problem on a two dimensional bounded or unbounded domain Omega with analytic boundary partial differential partial derivative Omega having at least one bounded connected component {-Delta u = g(u) in Omega, partial derivative u/partial derivative v = 0 and u = c on partial derivative Omega where c is a constant. When g(c) = 0 the constant solution u equivalent to c is the unique solution. For g(c) not equal 0, we show that the boundary is a circle if and only if the problem admits a solution that has a constant third or fourth normal derivative along the boundary. A similar result involving the fifth normal derivative is proved. Boundary-value-problems Overdetermined problems Pompeiu problem Radial symmetry Lucia, Marcello verfasserin (DE-588)1165083825 (DE-627)1029272301 (DE-576)510238769 aut Enthalten in Journal d'analyse mathématique Berlin : Springer, 1951 Volume 142(2020), Issue 2, pp. 667-696 Online-Ressource (DE-627)53027728X (DE-600)2316542-X (DE-576)264951751 1565-8538 nnns volume:142 year:2020 number:2 pages:667-696 Erscheint auch als Preprint Some results related to Schiffer's problem Oberwolfach-Walke : Mathematisches Forschungsinstitut, 2018 1 Online-Ressource (34 Seiten) (DE-627)1655292412 (DE-576)510238882 https://doi.org/10.1007/s11854-020-0146-z Resolving-System Full Text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 142 2020 2 667-696 Volume 142(2020), Issue 2, pp. 667-696 2088 01 DE-Frei3c 4269364009 00 --%%-- --%%-- --%%-- n Funding text/Acknowledgements: This research was begun during a "Research in Pairs" stay from May 23 to June 14, 2013 at Mathematisches Forschungsinstitut Oberwolfach. We are grateful to MFO and their staff for the excellent working conditions and hospitality. [...] l01 09-02-23 2088 01 DE-Frei3c Oberwolfach Preprint https://doi.org/10.14760/OWP-2018-18 2088 01 DE-Frei3c 00 (DE-627)1295034905 AMS:35 Partial differential equations |
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10.1007/s11854-020-0146-z doi (DE-627)1833787552 (DE-599)KXP1833787552 DE-627 ger DE-627 rda eng 35J25 msc 35N25 msc 35J61 msc 35P99 msc Kawohl, Bernhard 1952- verfasserin (DE-588)142802883 (DE-627)640131042 (DE-576)161668852 aut Some results related to Schiffer's problem Published: 26 January 2021 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 09.02.2023 We consider the following semilinear overdetermined problem on a two dimensional bounded or unbounded domain Omega with analytic boundary partial differential partial derivative Omega having at least one bounded connected component {-Delta u = g(u) in Omega, partial derivative u/partial derivative v = 0 and u = c on partial derivative Omega where c is a constant. When g(c) = 0 the constant solution u equivalent to c is the unique solution. For g(c) not equal 0, we show that the boundary is a circle if and only if the problem admits a solution that has a constant third or fourth normal derivative along the boundary. A similar result involving the fifth normal derivative is proved. Boundary-value-problems Overdetermined problems Pompeiu problem Radial symmetry Lucia, Marcello verfasserin (DE-588)1165083825 (DE-627)1029272301 (DE-576)510238769 aut Enthalten in Journal d'analyse mathématique Berlin : Springer, 1951 Volume 142(2020), Issue 2, pp. 667-696 Online-Ressource (DE-627)53027728X (DE-600)2316542-X (DE-576)264951751 1565-8538 nnns volume:142 year:2020 number:2 pages:667-696 Erscheint auch als Preprint Some results related to Schiffer's problem Oberwolfach-Walke : Mathematisches Forschungsinstitut, 2018 1 Online-Ressource (34 Seiten) (DE-627)1655292412 (DE-576)510238882 https://doi.org/10.1007/s11854-020-0146-z Resolving-System Full Text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 142 2020 2 667-696 Volume 142(2020), Issue 2, pp. 667-696 2088 01 DE-Frei3c 4269364009 00 --%%-- --%%-- --%%-- n Funding text/Acknowledgements: This research was begun during a "Research in Pairs" stay from May 23 to June 14, 2013 at Mathematisches Forschungsinstitut Oberwolfach. We are grateful to MFO and their staff for the excellent working conditions and hospitality. [...] l01 09-02-23 2088 01 DE-Frei3c Oberwolfach Preprint https://doi.org/10.14760/OWP-2018-18 2088 01 DE-Frei3c 00 (DE-627)1295034905 AMS:35 Partial differential equations |
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10.1007/s11854-020-0146-z doi (DE-627)1833787552 (DE-599)KXP1833787552 DE-627 ger DE-627 rda eng 35J25 msc 35N25 msc 35J61 msc 35P99 msc Kawohl, Bernhard 1952- verfasserin (DE-588)142802883 (DE-627)640131042 (DE-576)161668852 aut Some results related to Schiffer's problem Published: 26 January 2021 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 09.02.2023 We consider the following semilinear overdetermined problem on a two dimensional bounded or unbounded domain Omega with analytic boundary partial differential partial derivative Omega having at least one bounded connected component {-Delta u = g(u) in Omega, partial derivative u/partial derivative v = 0 and u = c on partial derivative Omega where c is a constant. When g(c) = 0 the constant solution u equivalent to c is the unique solution. For g(c) not equal 0, we show that the boundary is a circle if and only if the problem admits a solution that has a constant third or fourth normal derivative along the boundary. A similar result involving the fifth normal derivative is proved. Boundary-value-problems Overdetermined problems Pompeiu problem Radial symmetry Lucia, Marcello verfasserin (DE-588)1165083825 (DE-627)1029272301 (DE-576)510238769 aut Enthalten in Journal d'analyse mathématique Berlin : Springer, 1951 Volume 142(2020), Issue 2, pp. 667-696 Online-Ressource (DE-627)53027728X (DE-600)2316542-X (DE-576)264951751 1565-8538 nnns volume:142 year:2020 number:2 pages:667-696 Erscheint auch als Preprint Some results related to Schiffer's problem Oberwolfach-Walke : Mathematisches Forschungsinstitut, 2018 1 Online-Ressource (34 Seiten) (DE-627)1655292412 (DE-576)510238882 https://doi.org/10.1007/s11854-020-0146-z Resolving-System Full Text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 142 2020 2 667-696 Volume 142(2020), Issue 2, pp. 667-696 2088 01 DE-Frei3c 4269364009 00 --%%-- --%%-- --%%-- n Funding text/Acknowledgements: This research was begun during a "Research in Pairs" stay from May 23 to June 14, 2013 at Mathematisches Forschungsinstitut Oberwolfach. We are grateful to MFO and their staff for the excellent working conditions and hospitality. [...] l01 09-02-23 2088 01 DE-Frei3c Oberwolfach Preprint https://doi.org/10.14760/OWP-2018-18 2088 01 DE-Frei3c 00 (DE-627)1295034905 AMS:35 Partial differential equations |
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When g(c) = 0 the constant solution u equivalent to c is the unique solution. For g(c) not equal 0, we show that the boundary is a circle if and only if the problem admits a solution that has a constant third or fourth normal derivative along the boundary. 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Some results related to Schiffer's problem |
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2088@Funding text/Acknowledgements: This research was begun during a "Research in Pairs" stay from May 23 to June 14, 2013 at Mathematisches Forschungsinstitut Oberwolfach. We are grateful to MFO and their staff for the excellent working conditions and hospitality. [...] |
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Some results related to Schiffer's problem |
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Kawohl, Bernhard 1952- |
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some results related to schiffer's problem |
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Some results related to Schiffer's problem |
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We consider the following semilinear overdetermined problem on a two dimensional bounded or unbounded domain Omega with analytic boundary partial differential partial derivative Omega having at least one bounded connected component {-Delta u = g(u) in Omega, partial derivative u/partial derivative v = 0 and u = c on partial derivative Omega where c is a constant. When g(c) = 0 the constant solution u equivalent to c is the unique solution. For g(c) not equal 0, we show that the boundary is a circle if and only if the problem admits a solution that has a constant third or fourth normal derivative along the boundary. A similar result involving the fifth normal derivative is proved. Last seen: 09.02.2023 |
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We consider the following semilinear overdetermined problem on a two dimensional bounded or unbounded domain Omega with analytic boundary partial differential partial derivative Omega having at least one bounded connected component {-Delta u = g(u) in Omega, partial derivative u/partial derivative v = 0 and u = c on partial derivative Omega where c is a constant. When g(c) = 0 the constant solution u equivalent to c is the unique solution. For g(c) not equal 0, we show that the boundary is a circle if and only if the problem admits a solution that has a constant third or fourth normal derivative along the boundary. A similar result involving the fifth normal derivative is proved. Last seen: 09.02.2023 |
| abstract_unstemmed |
We consider the following semilinear overdetermined problem on a two dimensional bounded or unbounded domain Omega with analytic boundary partial differential partial derivative Omega having at least one bounded connected component {-Delta u = g(u) in Omega, partial derivative u/partial derivative v = 0 and u = c on partial derivative Omega where c is a constant. When g(c) = 0 the constant solution u equivalent to c is the unique solution. For g(c) not equal 0, we show that the boundary is a circle if and only if the problem admits a solution that has a constant third or fourth normal derivative along the boundary. A similar result involving the fifth normal derivative is proved. Last seen: 09.02.2023 |
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Some results related to Schiffer's problem |
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We are grateful to MFO and their staff for the excellent working conditions and hospitality. [...]</subfield><subfield code="y">l01</subfield><subfield code="z">09-02-23</subfield></datafield><datafield tag="981" ind1=" " ind2=" "><subfield code="2">2088</subfield><subfield code="1">01</subfield><subfield code="x">DE-Frei3c</subfield><subfield code="y">Oberwolfach Preprint</subfield><subfield code="r">https://doi.org/10.14760/OWP-2018-18</subfield></datafield><datafield tag="983" ind1=" " ind2=" "><subfield code="2">2088</subfield><subfield code="1">01</subfield><subfield code="x">DE-Frei3c</subfield><subfield code="8">00</subfield><subfield code="0">(DE-627)1295034905</subfield><subfield code="a">AMS:35</subfield><subfield code="b">Partial differential equations</subfield></datafield></record></collection>
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