Nonlocal operators of small order

Abstract In this work we study nonlocal operators and corresponding spaces with a focus on operators of order near zero. We investigate the interior regularity of eigenfunctions and of weak solutions to the associated Poisson problem depending on the regularity of the right-hand side. Our method exp...
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Gespeichert in:

Autor*in:	Feulefack, Pierre Aime [verfasserIn] Jarohs, Sven

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Nonlocal operators Regularity Nonlocal function spaces

Anmerkung:	© The Author(s) 2022

Übergeordnetes Werk:	Enthalten in: Annali di matematica pura ed applicata - Berlin : Springer, 1858, 202(2022), 4 vom: 15. Dez., Seite 1501-1529
Übergeordnetes Werk:	volume:202 ; year:2022 ; number:4 ; day:15 ; month:12 ; pages:1501-1529

Links:	Volltext

DOI / URN:	10.1007/s10231-022-01290-y

Katalog-ID:	SPR051768585

Internformat


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100	1		\|a Feulefack, Pierre Aime \|e verfasserin \|4 aut
245	1	0	\|a Nonlocal operators of small order
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520			\|a Abstract In this work we study nonlocal operators and corresponding spaces with a focus on operators of order near zero. We investigate the interior regularity of eigenfunctions and of weak solutions to the associated Poisson problem depending on the regularity of the right-hand side. Our method exploits the variational structure of the problem and we prove that eigenfunctions are of class %$C^{\infty }%$ if the kernel satisfies this property away from its singularity. Similarly in this case, if in the Poisson problem the right-hand is of class %$C^{\infty }%$, then also any weak solution is of class %$C^{\infty }%$.
650		4	\|a Nonlocal operators \|7 (dpeaa)DE-He213
650		4	\|a Regularity \|7 (dpeaa)DE-He213
650		4	\|a Nonlocal function spaces \|7 (dpeaa)DE-He213
700	1		\|a Jarohs, Sven \|0 (orcid)0000-0002-0490-861X \|4 aut
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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_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_267
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_2088
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_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
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952			\|d 202 \|j 2022 \|e 4 \|b 15 \|c 12 \|h 1501-1529

Indexfelder

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publishDate	2022
allfields	10.1007/s10231-022-01290-y doi (DE-627)SPR051768585 (SPR)s10231-022-01290-y-e DE-627 ger DE-627 rakwb eng Feulefack, Pierre Aime verfasserin aut Nonlocal operators of small order 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this work we study nonlocal operators and corresponding spaces with a focus on operators of order near zero. We investigate the interior regularity of eigenfunctions and of weak solutions to the associated Poisson problem depending on the regularity of the right-hand side. Our method exploits the variational structure of the problem and we prove that eigenfunctions are of class %$C^{\infty }%$ if the kernel satisfies this property away from its singularity. Similarly in this case, if in the Poisson problem the right-hand is of class %$C^{\infty }%$, then also any weak solution is of class %$C^{\infty }%$. Nonlocal operators (dpeaa)DE-He213 Regularity (dpeaa)DE-He213 Nonlocal function spaces (dpeaa)DE-He213 Jarohs, Sven (orcid)0000-0002-0490-861X aut Enthalten in Annali di matematica pura ed applicata Berlin : Springer, 1858 202(2022), 4 vom: 15. Dez., Seite 1501-1529 (DE-627)330615289 (DE-600)2049996-6 1618-1891 nnns volume:202 year:2022 number:4 day:15 month:12 pages:1501-1529 https://dx.doi.org/10.1007/s10231-022-01290-y kostenfrei 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_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_267 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_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_2118 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 202 2022 4 15 12 1501-1529
spelling	10.1007/s10231-022-01290-y doi (DE-627)SPR051768585 (SPR)s10231-022-01290-y-e DE-627 ger DE-627 rakwb eng Feulefack, Pierre Aime verfasserin aut Nonlocal operators of small order 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this work we study nonlocal operators and corresponding spaces with a focus on operators of order near zero. We investigate the interior regularity of eigenfunctions and of weak solutions to the associated Poisson problem depending on the regularity of the right-hand side. Our method exploits the variational structure of the problem and we prove that eigenfunctions are of class %$C^{\infty }%$ if the kernel satisfies this property away from its singularity. Similarly in this case, if in the Poisson problem the right-hand is of class %$C^{\infty }%$, then also any weak solution is of class %$C^{\infty }%$. Nonlocal operators (dpeaa)DE-He213 Regularity (dpeaa)DE-He213 Nonlocal function spaces (dpeaa)DE-He213 Jarohs, Sven (orcid)0000-0002-0490-861X aut Enthalten in Annali di matematica pura ed applicata Berlin : Springer, 1858 202(2022), 4 vom: 15. Dez., Seite 1501-1529 (DE-627)330615289 (DE-600)2049996-6 1618-1891 nnns volume:202 year:2022 number:4 day:15 month:12 pages:1501-1529 https://dx.doi.org/10.1007/s10231-022-01290-y kostenfrei 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_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_267 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_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_2118 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 202 2022 4 15 12 1501-1529
allfields_unstemmed	10.1007/s10231-022-01290-y doi (DE-627)SPR051768585 (SPR)s10231-022-01290-y-e DE-627 ger DE-627 rakwb eng Feulefack, Pierre Aime verfasserin aut Nonlocal operators of small order 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this work we study nonlocal operators and corresponding spaces with a focus on operators of order near zero. We investigate the interior regularity of eigenfunctions and of weak solutions to the associated Poisson problem depending on the regularity of the right-hand side. Our method exploits the variational structure of the problem and we prove that eigenfunctions are of class %$C^{\infty }%$ if the kernel satisfies this property away from its singularity. Similarly in this case, if in the Poisson problem the right-hand is of class %$C^{\infty }%$, then also any weak solution is of class %$C^{\infty }%$. Nonlocal operators (dpeaa)DE-He213 Regularity (dpeaa)DE-He213 Nonlocal function spaces (dpeaa)DE-He213 Jarohs, Sven (orcid)0000-0002-0490-861X aut Enthalten in Annali di matematica pura ed applicata Berlin : Springer, 1858 202(2022), 4 vom: 15. Dez., Seite 1501-1529 (DE-627)330615289 (DE-600)2049996-6 1618-1891 nnns volume:202 year:2022 number:4 day:15 month:12 pages:1501-1529 https://dx.doi.org/10.1007/s10231-022-01290-y kostenfrei 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_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_267 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_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_2118 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 202 2022 4 15 12 1501-1529
allfieldsGer	10.1007/s10231-022-01290-y doi (DE-627)SPR051768585 (SPR)s10231-022-01290-y-e DE-627 ger DE-627 rakwb eng Feulefack, Pierre Aime verfasserin aut Nonlocal operators of small order 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this work we study nonlocal operators and corresponding spaces with a focus on operators of order near zero. We investigate the interior regularity of eigenfunctions and of weak solutions to the associated Poisson problem depending on the regularity of the right-hand side. Our method exploits the variational structure of the problem and we prove that eigenfunctions are of class %$C^{\infty }%$ if the kernel satisfies this property away from its singularity. Similarly in this case, if in the Poisson problem the right-hand is of class %$C^{\infty }%$, then also any weak solution is of class %$C^{\infty }%$. Nonlocal operators (dpeaa)DE-He213 Regularity (dpeaa)DE-He213 Nonlocal function spaces (dpeaa)DE-He213 Jarohs, Sven (orcid)0000-0002-0490-861X aut Enthalten in Annali di matematica pura ed applicata Berlin : Springer, 1858 202(2022), 4 vom: 15. Dez., Seite 1501-1529 (DE-627)330615289 (DE-600)2049996-6 1618-1891 nnns volume:202 year:2022 number:4 day:15 month:12 pages:1501-1529 https://dx.doi.org/10.1007/s10231-022-01290-y kostenfrei 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_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_267 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_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_2118 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 202 2022 4 15 12 1501-1529
allfieldsSound	10.1007/s10231-022-01290-y doi (DE-627)SPR051768585 (SPR)s10231-022-01290-y-e DE-627 ger DE-627 rakwb eng Feulefack, Pierre Aime verfasserin aut Nonlocal operators of small order 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this work we study nonlocal operators and corresponding spaces with a focus on operators of order near zero. We investigate the interior regularity of eigenfunctions and of weak solutions to the associated Poisson problem depending on the regularity of the right-hand side. Our method exploits the variational structure of the problem and we prove that eigenfunctions are of class %$C^{\infty }%$ if the kernel satisfies this property away from its singularity. Similarly in this case, if in the Poisson problem the right-hand is of class %$C^{\infty }%$, then also any weak solution is of class %$C^{\infty }%$. Nonlocal operators (dpeaa)DE-He213 Regularity (dpeaa)DE-He213 Nonlocal function spaces (dpeaa)DE-He213 Jarohs, Sven (orcid)0000-0002-0490-861X aut Enthalten in Annali di matematica pura ed applicata Berlin : Springer, 1858 202(2022), 4 vom: 15. Dez., Seite 1501-1529 (DE-627)330615289 (DE-600)2049996-6 1618-1891 nnns volume:202 year:2022 number:4 day:15 month:12 pages:1501-1529 https://dx.doi.org/10.1007/s10231-022-01290-y kostenfrei 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_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_267 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_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_2118 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 202 2022 4 15 12 1501-1529
language	English
source	Enthalten in Annali di matematica pura ed applicata 202(2022), 4 vom: 15. Dez., Seite 1501-1529 volume:202 year:2022 number:4 day:15 month:12 pages:1501-1529
sourceStr	Enthalten in Annali di matematica pura ed applicata 202(2022), 4 vom: 15. Dez., Seite 1501-1529 volume:202 year:2022 number:4 day:15 month:12 pages:1501-1529
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Nonlocal operators Regularity Nonlocal function spaces
isfreeaccess_bool	true
container_title	Annali di matematica pura ed applicata
authorswithroles_txt_mv	Feulefack, Pierre Aime @@aut@@ Jarohs, Sven @@aut@@
publishDateDaySort_date	2022-12-15T00:00:00Z
hierarchy_top_id	330615289
id	SPR051768585
language_de	englisch
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author	Feulefack, Pierre Aime
spellingShingle	Feulefack, Pierre Aime misc Nonlocal operators misc Regularity misc Nonlocal function spaces Nonlocal operators of small order
authorStr	Feulefack, Pierre Aime
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topic_title	Nonlocal operators of small order Nonlocal operators (dpeaa)DE-He213 Regularity (dpeaa)DE-He213 Nonlocal function spaces (dpeaa)DE-He213
topic	misc Nonlocal operators misc Regularity misc Nonlocal function spaces
topic_unstemmed	misc Nonlocal operators misc Regularity misc Nonlocal function spaces
topic_browse	misc Nonlocal operators misc Regularity misc Nonlocal function spaces
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title	Nonlocal operators of small order
ctrlnum	(DE-627)SPR051768585 (SPR)s10231-022-01290-y-e
title_full	Nonlocal operators of small order
author_sort	Feulefack, Pierre Aime
journal	Annali di matematica pura ed applicata
journalStr	Annali di matematica pura ed applicata
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author_browse	Feulefack, Pierre Aime Jarohs, Sven
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author-letter	Feulefack, Pierre Aime
doi_str_mv	10.1007/s10231-022-01290-y
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normlink_prefix_str_mv	(orcid)0000-0002-0490-861X
title_sort	nonlocal operators of small order
title_auth	Nonlocal operators of small order
abstract	Abstract In this work we study nonlocal operators and corresponding spaces with a focus on operators of order near zero. We investigate the interior regularity of eigenfunctions and of weak solutions to the associated Poisson problem depending on the regularity of the right-hand side. Our method exploits the variational structure of the problem and we prove that eigenfunctions are of class %$C^{\infty }%$ if the kernel satisfies this property away from its singularity. Similarly in this case, if in the Poisson problem the right-hand is of class %$C^{\infty }%$, then also any weak solution is of class %$C^{\infty }%$. © The Author(s) 2022
abstractGer	Abstract In this work we study nonlocal operators and corresponding spaces with a focus on operators of order near zero. We investigate the interior regularity of eigenfunctions and of weak solutions to the associated Poisson problem depending on the regularity of the right-hand side. Our method exploits the variational structure of the problem and we prove that eigenfunctions are of class %$C^{\infty }%$ if the kernel satisfies this property away from its singularity. Similarly in this case, if in the Poisson problem the right-hand is of class %$C^{\infty }%$, then also any weak solution is of class %$C^{\infty }%$. © The Author(s) 2022
abstract_unstemmed	Abstract In this work we study nonlocal operators and corresponding spaces with a focus on operators of order near zero. We investigate the interior regularity of eigenfunctions and of weak solutions to the associated Poisson problem depending on the regularity of the right-hand side. Our method exploits the variational structure of the problem and we prove that eigenfunctions are of class %$C^{\infty }%$ if the kernel satisfies this property away from its singularity. Similarly in this case, if in the Poisson problem the right-hand is of class %$C^{\infty }%$, then also any weak solution is of class %$C^{\infty }%$. © The Author(s) 2022
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title_short	Nonlocal operators of small order
url	https://dx.doi.org/10.1007/s10231-022-01290-y
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author2	Jarohs, Sven
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doi_str	10.1007/s10231-022-01290-y
up_date	2024-07-03T23:41:16.522Z
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We investigate the interior regularity of eigenfunctions and of weak solutions to the associated Poisson problem depending on the regularity of the right-hand side. Our method exploits the variational structure of the problem and we prove that eigenfunctions are of class %$C^{\infty }%$ if the kernel satisfies this property away from its singularity. 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Nonlocal operators of small order

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