Zero volume boundary for extension domains from Sobolev to BV

Abstract In this note, we prove that the boundary of a $$(W^{1, p}, BV)$$-extension domain is of volume zero under the assumption that the domain $${\Omega }$$ is 1-fat at almost every $$x\in \partial {\Omega }$$. Especially, the boundary of any planar $$(W^{1, p}, BV)$$-extension domain is of volum...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Rajala, Tapio [verfasserIn] Zhu, Zheng [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2024

Schlagwörter:	Extension domains Sobolev functions BV functions Boundary volume

Anmerkung:	© The Author(s) 2024

Übergeordnetes Werk:	Enthalten in: Revista matemática complutense - Springer International Publishing, 1988, 37(2024), 3 vom: 08. Feb., Seite 819-831
Übergeordnetes Werk:	volume:37 ; year:2024 ; number:3 ; day:08 ; month:02 ; pages:819-831

Links:	Volltext

DOI / URN:	10.1007/s13163-024-00485-6

Katalog-ID:	SPR05746295X

Internformat


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520			\|a Abstract In this note, we prove that the boundary of a $$(W^{1, p}, BV)$$-extension domain is of volume zero under the assumption that the domain $${\Omega }$$ is 1-fat at almost every $$x\in \partial {\Omega }$$. Especially, the boundary of any planar $$(W^{1, p}, BV)$$-extension domain is of volume zero.
650		4	\|a Extension domains \|7 (dpeaa)DE-He213
650		4	\|a Sobolev functions \|7 (dpeaa)DE-He213
650		4	\|a BV functions \|7 (dpeaa)DE-He213
650		4	\|a Boundary volume \|7 (dpeaa)DE-He213
700	1		\|a Zhu, Zheng \|e verfasserin \|4 aut
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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_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_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_2574
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
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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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allfields	10.1007/s13163-024-00485-6 doi (DE-627)SPR05746295X (SPR)s13163-024-00485-6-e DE-627 ger DE-627 rakwb eng 510 VZ 31.00 bkl Rajala, Tapio verfasserin (orcid)0000-0001-6450-9656 aut Zero volume boundary for extension domains from Sobolev to BV 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract In this note, we prove that the boundary of a $$(W^{1, p}, BV)$$-extension domain is of volume zero under the assumption that the domain $${\Omega }$$ is 1-fat at almost every $$x\in \partial {\Omega }$$. Especially, the boundary of any planar $$(W^{1, p}, BV)$$-extension domain is of volume zero. Extension domains (dpeaa)DE-He213 Sobolev functions (dpeaa)DE-He213 BV functions (dpeaa)DE-He213 Boundary volume (dpeaa)DE-He213 Zhu, Zheng verfasserin aut Enthalten in Revista matemática complutense Springer International Publishing, 1988 37(2024), 3 vom: 08. Feb., Seite 819-831 (DE-627)327098120 (DE-600)2043797-3 1988-2807 nnns volume:37 year:2024 number:3 day:08 month:02 pages:819-831 https://dx.doi.org/10.1007/s13163-024-00485-6 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_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_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_2574 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 31.00 VZ AR 37 2024 3 08 02 819-831
spelling	10.1007/s13163-024-00485-6 doi (DE-627)SPR05746295X (SPR)s13163-024-00485-6-e DE-627 ger DE-627 rakwb eng 510 VZ 31.00 bkl Rajala, Tapio verfasserin (orcid)0000-0001-6450-9656 aut Zero volume boundary for extension domains from Sobolev to BV 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract In this note, we prove that the boundary of a $$(W^{1, p}, BV)$$-extension domain is of volume zero under the assumption that the domain $${\Omega }$$ is 1-fat at almost every $$x\in \partial {\Omega }$$. Especially, the boundary of any planar $$(W^{1, p}, BV)$$-extension domain is of volume zero. Extension domains (dpeaa)DE-He213 Sobolev functions (dpeaa)DE-He213 BV functions (dpeaa)DE-He213 Boundary volume (dpeaa)DE-He213 Zhu, Zheng verfasserin aut Enthalten in Revista matemática complutense Springer International Publishing, 1988 37(2024), 3 vom: 08. Feb., Seite 819-831 (DE-627)327098120 (DE-600)2043797-3 1988-2807 nnns volume:37 year:2024 number:3 day:08 month:02 pages:819-831 https://dx.doi.org/10.1007/s13163-024-00485-6 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_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_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_2574 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 31.00 VZ AR 37 2024 3 08 02 819-831
allfields_unstemmed	10.1007/s13163-024-00485-6 doi (DE-627)SPR05746295X (SPR)s13163-024-00485-6-e DE-627 ger DE-627 rakwb eng 510 VZ 31.00 bkl Rajala, Tapio verfasserin (orcid)0000-0001-6450-9656 aut Zero volume boundary for extension domains from Sobolev to BV 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract In this note, we prove that the boundary of a $$(W^{1, p}, BV)$$-extension domain is of volume zero under the assumption that the domain $${\Omega }$$ is 1-fat at almost every $$x\in \partial {\Omega }$$. Especially, the boundary of any planar $$(W^{1, p}, BV)$$-extension domain is of volume zero. Extension domains (dpeaa)DE-He213 Sobolev functions (dpeaa)DE-He213 BV functions (dpeaa)DE-He213 Boundary volume (dpeaa)DE-He213 Zhu, Zheng verfasserin aut Enthalten in Revista matemática complutense Springer International Publishing, 1988 37(2024), 3 vom: 08. Feb., Seite 819-831 (DE-627)327098120 (DE-600)2043797-3 1988-2807 nnns volume:37 year:2024 number:3 day:08 month:02 pages:819-831 https://dx.doi.org/10.1007/s13163-024-00485-6 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_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_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_2574 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 31.00 VZ AR 37 2024 3 08 02 819-831
allfieldsGer	10.1007/s13163-024-00485-6 doi (DE-627)SPR05746295X (SPR)s13163-024-00485-6-e DE-627 ger DE-627 rakwb eng 510 VZ 31.00 bkl Rajala, Tapio verfasserin (orcid)0000-0001-6450-9656 aut Zero volume boundary for extension domains from Sobolev to BV 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract In this note, we prove that the boundary of a $$(W^{1, p}, BV)$$-extension domain is of volume zero under the assumption that the domain $${\Omega }$$ is 1-fat at almost every $$x\in \partial {\Omega }$$. Especially, the boundary of any planar $$(W^{1, p}, BV)$$-extension domain is of volume zero. Extension domains (dpeaa)DE-He213 Sobolev functions (dpeaa)DE-He213 BV functions (dpeaa)DE-He213 Boundary volume (dpeaa)DE-He213 Zhu, Zheng verfasserin aut Enthalten in Revista matemática complutense Springer International Publishing, 1988 37(2024), 3 vom: 08. Feb., Seite 819-831 (DE-627)327098120 (DE-600)2043797-3 1988-2807 nnns volume:37 year:2024 number:3 day:08 month:02 pages:819-831 https://dx.doi.org/10.1007/s13163-024-00485-6 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_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_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_2574 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 31.00 VZ AR 37 2024 3 08 02 819-831
allfieldsSound	10.1007/s13163-024-00485-6 doi (DE-627)SPR05746295X (SPR)s13163-024-00485-6-e DE-627 ger DE-627 rakwb eng 510 VZ 31.00 bkl Rajala, Tapio verfasserin (orcid)0000-0001-6450-9656 aut Zero volume boundary for extension domains from Sobolev to BV 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract In this note, we prove that the boundary of a $$(W^{1, p}, BV)$$-extension domain is of volume zero under the assumption that the domain $${\Omega }$$ is 1-fat at almost every $$x\in \partial {\Omega }$$. Especially, the boundary of any planar $$(W^{1, p}, BV)$$-extension domain is of volume zero. Extension domains (dpeaa)DE-He213 Sobolev functions (dpeaa)DE-He213 BV functions (dpeaa)DE-He213 Boundary volume (dpeaa)DE-He213 Zhu, Zheng verfasserin aut Enthalten in Revista matemática complutense Springer International Publishing, 1988 37(2024), 3 vom: 08. Feb., Seite 819-831 (DE-627)327098120 (DE-600)2043797-3 1988-2807 nnns volume:37 year:2024 number:3 day:08 month:02 pages:819-831 https://dx.doi.org/10.1007/s13163-024-00485-6 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_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_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_2574 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 31.00 VZ AR 37 2024 3 08 02 819-831
language	English
source	Enthalten in Revista matemática complutense 37(2024), 3 vom: 08. Feb., Seite 819-831 volume:37 year:2024 number:3 day:08 month:02 pages:819-831
sourceStr	Enthalten in Revista matemática complutense 37(2024), 3 vom: 08. Feb., Seite 819-831 volume:37 year:2024 number:3 day:08 month:02 pages:819-831
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Extension domains Sobolev functions BV functions Boundary volume
dewey-raw	510
isfreeaccess_bool	true
container_title	Revista matemática complutense
authorswithroles_txt_mv	Rajala, Tapio @@aut@@ Zhu, Zheng @@aut@@
publishDateDaySort_date	2024-02-08T00:00:00Z
hierarchy_top_id	327098120
dewey-sort	3510
id	SPR05746295X
language_de	englisch
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author	Rajala, Tapio
spellingShingle	Rajala, Tapio ddc 510 bkl 31.00 misc Extension domains misc Sobolev functions misc BV functions misc Boundary volume Zero volume boundary for extension domains from Sobolev to BV
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topic_title	510 VZ 31.00 bkl Zero volume boundary for extension domains from Sobolev to BV Extension domains (dpeaa)DE-He213 Sobolev functions (dpeaa)DE-He213 BV functions (dpeaa)DE-He213 Boundary volume (dpeaa)DE-He213
topic	ddc 510 bkl 31.00 misc Extension domains misc Sobolev functions misc BV functions misc Boundary volume
topic_unstemmed	ddc 510 bkl 31.00 misc Extension domains misc Sobolev functions misc BV functions misc Boundary volume
topic_browse	ddc 510 bkl 31.00 misc Extension domains misc Sobolev functions misc BV functions misc Boundary volume
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title	Zero volume boundary for extension domains from Sobolev to BV
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title_full	Zero volume boundary for extension domains from Sobolev to BV
author_sort	Rajala, Tapio
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author_browse	Rajala, Tapio Zhu, Zheng
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title_sort	zero volume boundary for extension domains from sobolev to bv
title_auth	Zero volume boundary for extension domains from Sobolev to BV
abstract	Abstract In this note, we prove that the boundary of a $$(W^{1, p}, BV)$$-extension domain is of volume zero under the assumption that the domain $${\Omega }$$ is 1-fat at almost every $$x\in \partial {\Omega }$$. Especially, the boundary of any planar $$(W^{1, p}, BV)$$-extension domain is of volume zero. © The Author(s) 2024
abstractGer	Abstract In this note, we prove that the boundary of a $$(W^{1, p}, BV)$$-extension domain is of volume zero under the assumption that the domain $${\Omega }$$ is 1-fat at almost every $$x\in \partial {\Omega }$$. Especially, the boundary of any planar $$(W^{1, p}, BV)$$-extension domain is of volume zero. © The Author(s) 2024
abstract_unstemmed	Abstract In this note, we prove that the boundary of a $$(W^{1, p}, BV)$$-extension domain is of volume zero under the assumption that the domain $${\Omega }$$ is 1-fat at almost every $$x\in \partial {\Omega }$$. Especially, the boundary of any planar $$(W^{1, p}, BV)$$-extension domain is of volume zero. © The Author(s) 2024
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title_short	Zero volume boundary for extension domains from Sobolev to BV
url	https://dx.doi.org/10.1007/s13163-024-00485-6
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author2	Zhu, Zheng
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doi_str	10.1007/s13163-024-00485-6
up_date	2024-09-26T04:49:28.296Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">SPR05746295X</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20240926064729.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">240926s2024 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s13163-024-00485-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR05746295X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s13163-024-00485-6-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="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Rajala, Tapio</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0001-6450-9656</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Zero volume boundary for extension domains from Sobolev to BV</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2024</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">© The Author(s) 2024</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this note, we prove that the boundary of a $$(W^{1, p}, BV)$$-extension domain is of volume zero under the assumption that the domain $${\Omega }$$ is 1-fat at almost every $$x\in \partial {\Omega }$$. 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Zero volume boundary for extension domains from Sobolev to BV

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