Hypoellipticity for infinitely degenerate quasilinear equations and the dirichlet problem
Abstract In [10], we considered a class of infinitely degenerate quasilinear equations of the form div %$A(x,w)\nabla w + \overrightarrow r (x,w) \cdot \nabla w + f(x,w) = 0%$ and derived a priori bounds for high order derivatives Daw of their solutions in terms of w and ▿w. We now show that it is p...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Rios, Cristian [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© Hebrew University Magnes Press 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Journal d'analyse mathématique - Berlin : Springer, 1951, 119(2013), 1 vom: Apr., Seite 1-62 |
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| Übergeordnetes Werk: |
volume:119 ; year:2013 ; number:1 ; month:04 ; pages:1-62 |
| Links: |
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| DOI / URN: |
10.1007/s11854-013-0001-6 |
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| Katalog-ID: |
SPR022809864 |
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| 100 | 1 | |a Rios, Cristian |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Hypoellipticity for infinitely degenerate quasilinear equations and the dirichlet problem |
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| 520 | |a Abstract In [10], we considered a class of infinitely degenerate quasilinear equations of the form div %$A(x,w)\nabla w + \overrightarrow r (x,w) \cdot \nabla w + f(x,w) = 0%$ and derived a priori bounds for high order derivatives Daw of their solutions in terms of w and ▿w. We now show that it is possible to obtain bounds in terms of just w for a further subclass of such equations, and we apply the resulting estimates to prove that continuous weak solutions are necessarily smooth. We also obtain existence, uniqueness, and interior %${\varrho ^\infty }%$-regularity of solutions for the corresponding Dirichlet problem with continuous boundary data. | ||
| 650 | 4 | |a Weak Solution |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Dirichlet Problem |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Strong Solution |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Smooth Solution |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Sobolev Inequality |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Sawyer, Eric T. |4 aut | |
| 700 | 1 | |a Wheeden, Richard L. |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Journal d'analyse mathématique |d Berlin : Springer, 1951 |g 119(2013), 1 vom: Apr., Seite 1-62 |w (DE-627)53027728X |w (DE-600)2316542-X |x 1565-8538 |7 nnns |
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| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s11854-013-0001-6 |z lizenzpflichtig |3 Volltext |
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2013 |
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10.1007/s11854-013-0001-6 doi (DE-627)SPR022809864 (SPR)s11854-013-0001-6-e DE-627 ger DE-627 rakwb eng Rios, Cristian verfasserin aut Hypoellipticity for infinitely degenerate quasilinear equations and the dirichlet problem 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Hebrew University Magnes Press 2013 Abstract In [10], we considered a class of infinitely degenerate quasilinear equations of the form div %$A(x,w)\nabla w + \overrightarrow r (x,w) \cdot \nabla w + f(x,w) = 0%$ and derived a priori bounds for high order derivatives Daw of their solutions in terms of w and ▿w. We now show that it is possible to obtain bounds in terms of just w for a further subclass of such equations, and we apply the resulting estimates to prove that continuous weak solutions are necessarily smooth. We also obtain existence, uniqueness, and interior %${\varrho ^\infty }%$-regularity of solutions for the corresponding Dirichlet problem with continuous boundary data. Weak Solution (dpeaa)DE-He213 Dirichlet Problem (dpeaa)DE-He213 Strong Solution (dpeaa)DE-He213 Smooth Solution (dpeaa)DE-He213 Sobolev Inequality (dpeaa)DE-He213 Sawyer, Eric T. aut Wheeden, Richard L. aut Enthalten in Journal d'analyse mathématique Berlin : Springer, 1951 119(2013), 1 vom: Apr., Seite 1-62 (DE-627)53027728X (DE-600)2316542-X 1565-8538 nnns volume:119 year:2013 number:1 month:04 pages:1-62 https://dx.doi.org/10.1007/s11854-013-0001-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 119 2013 1 04 1-62 |
| spelling |
10.1007/s11854-013-0001-6 doi (DE-627)SPR022809864 (SPR)s11854-013-0001-6-e DE-627 ger DE-627 rakwb eng Rios, Cristian verfasserin aut Hypoellipticity for infinitely degenerate quasilinear equations and the dirichlet problem 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Hebrew University Magnes Press 2013 Abstract In [10], we considered a class of infinitely degenerate quasilinear equations of the form div %$A(x,w)\nabla w + \overrightarrow r (x,w) \cdot \nabla w + f(x,w) = 0%$ and derived a priori bounds for high order derivatives Daw of their solutions in terms of w and ▿w. We now show that it is possible to obtain bounds in terms of just w for a further subclass of such equations, and we apply the resulting estimates to prove that continuous weak solutions are necessarily smooth. We also obtain existence, uniqueness, and interior %${\varrho ^\infty }%$-regularity of solutions for the corresponding Dirichlet problem with continuous boundary data. Weak Solution (dpeaa)DE-He213 Dirichlet Problem (dpeaa)DE-He213 Strong Solution (dpeaa)DE-He213 Smooth Solution (dpeaa)DE-He213 Sobolev Inequality (dpeaa)DE-He213 Sawyer, Eric T. aut Wheeden, Richard L. aut Enthalten in Journal d'analyse mathématique Berlin : Springer, 1951 119(2013), 1 vom: Apr., Seite 1-62 (DE-627)53027728X (DE-600)2316542-X 1565-8538 nnns volume:119 year:2013 number:1 month:04 pages:1-62 https://dx.doi.org/10.1007/s11854-013-0001-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 119 2013 1 04 1-62 |
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10.1007/s11854-013-0001-6 doi (DE-627)SPR022809864 (SPR)s11854-013-0001-6-e DE-627 ger DE-627 rakwb eng Rios, Cristian verfasserin aut Hypoellipticity for infinitely degenerate quasilinear equations and the dirichlet problem 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Hebrew University Magnes Press 2013 Abstract In [10], we considered a class of infinitely degenerate quasilinear equations of the form div %$A(x,w)\nabla w + \overrightarrow r (x,w) \cdot \nabla w + f(x,w) = 0%$ and derived a priori bounds for high order derivatives Daw of their solutions in terms of w and ▿w. We now show that it is possible to obtain bounds in terms of just w for a further subclass of such equations, and we apply the resulting estimates to prove that continuous weak solutions are necessarily smooth. We also obtain existence, uniqueness, and interior %${\varrho ^\infty }%$-regularity of solutions for the corresponding Dirichlet problem with continuous boundary data. Weak Solution (dpeaa)DE-He213 Dirichlet Problem (dpeaa)DE-He213 Strong Solution (dpeaa)DE-He213 Smooth Solution (dpeaa)DE-He213 Sobolev Inequality (dpeaa)DE-He213 Sawyer, Eric T. aut Wheeden, Richard L. aut Enthalten in Journal d'analyse mathématique Berlin : Springer, 1951 119(2013), 1 vom: Apr., Seite 1-62 (DE-627)53027728X (DE-600)2316542-X 1565-8538 nnns volume:119 year:2013 number:1 month:04 pages:1-62 https://dx.doi.org/10.1007/s11854-013-0001-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 119 2013 1 04 1-62 |
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10.1007/s11854-013-0001-6 doi (DE-627)SPR022809864 (SPR)s11854-013-0001-6-e DE-627 ger DE-627 rakwb eng Rios, Cristian verfasserin aut Hypoellipticity for infinitely degenerate quasilinear equations and the dirichlet problem 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Hebrew University Magnes Press 2013 Abstract In [10], we considered a class of infinitely degenerate quasilinear equations of the form div %$A(x,w)\nabla w + \overrightarrow r (x,w) \cdot \nabla w + f(x,w) = 0%$ and derived a priori bounds for high order derivatives Daw of their solutions in terms of w and ▿w. We now show that it is possible to obtain bounds in terms of just w for a further subclass of such equations, and we apply the resulting estimates to prove that continuous weak solutions are necessarily smooth. We also obtain existence, uniqueness, and interior %${\varrho ^\infty }%$-regularity of solutions for the corresponding Dirichlet problem with continuous boundary data. Weak Solution (dpeaa)DE-He213 Dirichlet Problem (dpeaa)DE-He213 Strong Solution (dpeaa)DE-He213 Smooth Solution (dpeaa)DE-He213 Sobolev Inequality (dpeaa)DE-He213 Sawyer, Eric T. aut Wheeden, Richard L. aut Enthalten in Journal d'analyse mathématique Berlin : Springer, 1951 119(2013), 1 vom: Apr., Seite 1-62 (DE-627)53027728X (DE-600)2316542-X 1565-8538 nnns volume:119 year:2013 number:1 month:04 pages:1-62 https://dx.doi.org/10.1007/s11854-013-0001-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 119 2013 1 04 1-62 |
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10.1007/s11854-013-0001-6 doi (DE-627)SPR022809864 (SPR)s11854-013-0001-6-e DE-627 ger DE-627 rakwb eng Rios, Cristian verfasserin aut Hypoellipticity for infinitely degenerate quasilinear equations and the dirichlet problem 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Hebrew University Magnes Press 2013 Abstract In [10], we considered a class of infinitely degenerate quasilinear equations of the form div %$A(x,w)\nabla w + \overrightarrow r (x,w) \cdot \nabla w + f(x,w) = 0%$ and derived a priori bounds for high order derivatives Daw of their solutions in terms of w and ▿w. We now show that it is possible to obtain bounds in terms of just w for a further subclass of such equations, and we apply the resulting estimates to prove that continuous weak solutions are necessarily smooth. We also obtain existence, uniqueness, and interior %${\varrho ^\infty }%$-regularity of solutions for the corresponding Dirichlet problem with continuous boundary data. Weak Solution (dpeaa)DE-He213 Dirichlet Problem (dpeaa)DE-He213 Strong Solution (dpeaa)DE-He213 Smooth Solution (dpeaa)DE-He213 Sobolev Inequality (dpeaa)DE-He213 Sawyer, Eric T. aut Wheeden, Richard L. aut Enthalten in Journal d'analyse mathématique Berlin : Springer, 1951 119(2013), 1 vom: Apr., Seite 1-62 (DE-627)53027728X (DE-600)2316542-X 1565-8538 nnns volume:119 year:2013 number:1 month:04 pages:1-62 https://dx.doi.org/10.1007/s11854-013-0001-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 119 2013 1 04 1-62 |
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Rios, Cristian misc Weak Solution misc Dirichlet Problem misc Strong Solution misc Smooth Solution misc Sobolev Inequality Hypoellipticity for infinitely degenerate quasilinear equations and the dirichlet problem |
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Hypoellipticity for infinitely degenerate quasilinear equations and the dirichlet problem Weak Solution (dpeaa)DE-He213 Dirichlet Problem (dpeaa)DE-He213 Strong Solution (dpeaa)DE-He213 Smooth Solution (dpeaa)DE-He213 Sobolev Inequality (dpeaa)DE-He213 |
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hypoellipticity for infinitely degenerate quasilinear equations and the dirichlet problem |
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Hypoellipticity for infinitely degenerate quasilinear equations and the dirichlet problem |
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Abstract In [10], we considered a class of infinitely degenerate quasilinear equations of the form div %$A(x,w)\nabla w + \overrightarrow r (x,w) \cdot \nabla w + f(x,w) = 0%$ and derived a priori bounds for high order derivatives Daw of their solutions in terms of w and ▿w. We now show that it is possible to obtain bounds in terms of just w for a further subclass of such equations, and we apply the resulting estimates to prove that continuous weak solutions are necessarily smooth. We also obtain existence, uniqueness, and interior %${\varrho ^\infty }%$-regularity of solutions for the corresponding Dirichlet problem with continuous boundary data. © Hebrew University Magnes Press 2013 |
| abstractGer |
Abstract In [10], we considered a class of infinitely degenerate quasilinear equations of the form div %$A(x,w)\nabla w + \overrightarrow r (x,w) \cdot \nabla w + f(x,w) = 0%$ and derived a priori bounds for high order derivatives Daw of their solutions in terms of w and ▿w. We now show that it is possible to obtain bounds in terms of just w for a further subclass of such equations, and we apply the resulting estimates to prove that continuous weak solutions are necessarily smooth. We also obtain existence, uniqueness, and interior %${\varrho ^\infty }%$-regularity of solutions for the corresponding Dirichlet problem with continuous boundary data. © Hebrew University Magnes Press 2013 |
| abstract_unstemmed |
Abstract In [10], we considered a class of infinitely degenerate quasilinear equations of the form div %$A(x,w)\nabla w + \overrightarrow r (x,w) \cdot \nabla w + f(x,w) = 0%$ and derived a priori bounds for high order derivatives Daw of their solutions in terms of w and ▿w. We now show that it is possible to obtain bounds in terms of just w for a further subclass of such equations, and we apply the resulting estimates to prove that continuous weak solutions are necessarily smooth. We also obtain existence, uniqueness, and interior %${\varrho ^\infty }%$-regularity of solutions for the corresponding Dirichlet problem with continuous boundary data. © Hebrew University Magnes Press 2013 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR022809864</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230330070803.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201006s2013 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11854-013-0001-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR022809864</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s11854-013-0001-6-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Rios, Cristian</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Hypoellipticity for infinitely degenerate quasilinear equations and the dirichlet problem</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2013</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Hebrew University Magnes Press 2013</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In [10], we considered a class of infinitely degenerate quasilinear equations of the form div %$A(x,w)\nabla w + \overrightarrow r (x,w) \cdot \nabla w + f(x,w) = 0%$ and derived a priori bounds for high order derivatives Daw of their solutions in terms of w and ▿w. We now show that it is possible to obtain bounds in terms of just w for a further subclass of such equations, and we apply the resulting estimates to prove that continuous weak solutions are necessarily smooth. We also obtain existence, uniqueness, and interior %${\varrho ^\infty }%$-regularity of solutions for the corresponding Dirichlet problem with continuous boundary data.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Weak Solution</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Dirichlet Problem</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Strong Solution</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Smooth Solution</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sobolev Inequality</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Sawyer, Eric T.</subfield><subfield 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