Regularity for Quasi-Linear <i<p</i<-Laplacian Type Non-Homogeneous Equations in the Heisenberg Group

When <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<2</mn<<mo<−</mo<<mn<1</mn<<mo</</mo<<mi<Q</mi<<mo<<</mo<<mi<p</m...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Chengwei Yu [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	non-homogeneous equations Heisenberg group regularities Riesz potentials

Übergeordnetes Werk:	In: Mathematics - MDPI AG, 2013, 10(2022), 21, p 4129
Übergeordnetes Werk:	volume:10 ; year:2022 ; number:21, p 4129

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/math10214129

Katalog-ID:	DOAJ028680588

Internformat


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245	1	0	\|a Regularity for Quasi-Linear <i<p</i<-Laplacian Type Non-Homogeneous Equations in the Heisenberg Group
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520			\|a When <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<2</mn<<mo<−</mo<<mn<1</mn<<mo</</mo<<mi<Q</mi<<mo<<</mo<<mi<p</mi<<mo<≤</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, we establish the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<0</mn<<mo<,</mo<<mn<1</mn<</mrow<</msubsup<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<1</mn<<mo<,</mo<<mi<α</mi<</mrow<</msubsup<</semantics<</math<</inline-formula<-regularities of weak solutions to quasi-linear <i<p</i<-Laplacian type non-homogeneous equations in the Heisenberg group <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mo<=</mo<<mn<2</mn<<mi<n</mi<<mo<+</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula< is the homogeneous dimension of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<.
650		4	\|a <i<p</i<-Laplacian type
650		4	\|a non-homogeneous equations
650		4	\|a Heisenberg group
650		4	\|a regularities
650		4	\|a Riesz potentials
653		0	\|a Mathematics
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773	1	8	\|g volume:10 \|g year:2022 \|g number:21, p 4129
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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_95
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_151
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_213
912			\|a GBV_ILN_230
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4249
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_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4700
951			\|a AR
952			\|d 10 \|j 2022 \|e 21, p 4129

Indexfelder

author_variant	c y cy
matchkey_str	article:22277390:2022----::euaiyoqaiierplpainyeohmgnosqai
hierarchy_sort_str	2022
callnumber-subject-code	QA
publishDate	2022
allfields	10.3390/math10214129 doi (DE-627)DOAJ028680588 (DE-599)DOAJfc0ad0682e4c473cac2050ed4d65c3b1 DE-627 ger DE-627 rakwb eng QA1-939 Chengwei Yu verfasserin aut Regularity for Quasi-Linear <i<p</i<-Laplacian Type Non-Homogeneous Equations in the Heisenberg Group 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier When <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<2</mn<<mo<−</mo<<mn<1</mn<<mo</</mo<<mi<Q</mi<<mo<<</mo<<mi<p</mi<<mo<≤</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, we establish the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<0</mn<<mo<,</mo<<mn<1</mn<</mrow<</msubsup<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<1</mn<<mo<,</mo<<mi<α</mi<</mrow<</msubsup<</semantics<</math<</inline-formula<-regularities of weak solutions to quasi-linear <i<p</i<-Laplacian type non-homogeneous equations in the Heisenberg group <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mo<=</mo<<mn<2</mn<<mi<n</mi<<mo<+</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula< is the homogeneous dimension of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<. <i<p</i<-Laplacian type non-homogeneous equations Heisenberg group regularities Riesz potentials Mathematics In Mathematics MDPI AG, 2013 10(2022), 21, p 4129 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:10 year:2022 number:21, p 4129 https://doi.org/10.3390/math10214129 kostenfrei https://doaj.org/article/fc0ad0682e4c473cac2050ed4d65c3b1 kostenfrei https://www.mdpi.com/2227-7390/10/21/4129 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2022 21, p 4129
spelling	10.3390/math10214129 doi (DE-627)DOAJ028680588 (DE-599)DOAJfc0ad0682e4c473cac2050ed4d65c3b1 DE-627 ger DE-627 rakwb eng QA1-939 Chengwei Yu verfasserin aut Regularity for Quasi-Linear <i<p</i<-Laplacian Type Non-Homogeneous Equations in the Heisenberg Group 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier When <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<2</mn<<mo<−</mo<<mn<1</mn<<mo</</mo<<mi<Q</mi<<mo<<</mo<<mi<p</mi<<mo<≤</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, we establish the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<0</mn<<mo<,</mo<<mn<1</mn<</mrow<</msubsup<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<1</mn<<mo<,</mo<<mi<α</mi<</mrow<</msubsup<</semantics<</math<</inline-formula<-regularities of weak solutions to quasi-linear <i<p</i<-Laplacian type non-homogeneous equations in the Heisenberg group <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mo<=</mo<<mn<2</mn<<mi<n</mi<<mo<+</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula< is the homogeneous dimension of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<. <i<p</i<-Laplacian type non-homogeneous equations Heisenberg group regularities Riesz potentials Mathematics In Mathematics MDPI AG, 2013 10(2022), 21, p 4129 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:10 year:2022 number:21, p 4129 https://doi.org/10.3390/math10214129 kostenfrei https://doaj.org/article/fc0ad0682e4c473cac2050ed4d65c3b1 kostenfrei https://www.mdpi.com/2227-7390/10/21/4129 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2022 21, p 4129
allfields_unstemmed	10.3390/math10214129 doi (DE-627)DOAJ028680588 (DE-599)DOAJfc0ad0682e4c473cac2050ed4d65c3b1 DE-627 ger DE-627 rakwb eng QA1-939 Chengwei Yu verfasserin aut Regularity for Quasi-Linear <i<p</i<-Laplacian Type Non-Homogeneous Equations in the Heisenberg Group 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier When <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<2</mn<<mo<−</mo<<mn<1</mn<<mo</</mo<<mi<Q</mi<<mo<<</mo<<mi<p</mi<<mo<≤</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, we establish the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<0</mn<<mo<,</mo<<mn<1</mn<</mrow<</msubsup<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<1</mn<<mo<,</mo<<mi<α</mi<</mrow<</msubsup<</semantics<</math<</inline-formula<-regularities of weak solutions to quasi-linear <i<p</i<-Laplacian type non-homogeneous equations in the Heisenberg group <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mo<=</mo<<mn<2</mn<<mi<n</mi<<mo<+</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula< is the homogeneous dimension of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<. <i<p</i<-Laplacian type non-homogeneous equations Heisenberg group regularities Riesz potentials Mathematics In Mathematics MDPI AG, 2013 10(2022), 21, p 4129 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:10 year:2022 number:21, p 4129 https://doi.org/10.3390/math10214129 kostenfrei https://doaj.org/article/fc0ad0682e4c473cac2050ed4d65c3b1 kostenfrei https://www.mdpi.com/2227-7390/10/21/4129 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2022 21, p 4129
allfieldsGer	10.3390/math10214129 doi (DE-627)DOAJ028680588 (DE-599)DOAJfc0ad0682e4c473cac2050ed4d65c3b1 DE-627 ger DE-627 rakwb eng QA1-939 Chengwei Yu verfasserin aut Regularity for Quasi-Linear <i<p</i<-Laplacian Type Non-Homogeneous Equations in the Heisenberg Group 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier When <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<2</mn<<mo<−</mo<<mn<1</mn<<mo</</mo<<mi<Q</mi<<mo<<</mo<<mi<p</mi<<mo<≤</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, we establish the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<0</mn<<mo<,</mo<<mn<1</mn<</mrow<</msubsup<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<1</mn<<mo<,</mo<<mi<α</mi<</mrow<</msubsup<</semantics<</math<</inline-formula<-regularities of weak solutions to quasi-linear <i<p</i<-Laplacian type non-homogeneous equations in the Heisenberg group <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mo<=</mo<<mn<2</mn<<mi<n</mi<<mo<+</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula< is the homogeneous dimension of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<. <i<p</i<-Laplacian type non-homogeneous equations Heisenberg group regularities Riesz potentials Mathematics In Mathematics MDPI AG, 2013 10(2022), 21, p 4129 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:10 year:2022 number:21, p 4129 https://doi.org/10.3390/math10214129 kostenfrei https://doaj.org/article/fc0ad0682e4c473cac2050ed4d65c3b1 kostenfrei https://www.mdpi.com/2227-7390/10/21/4129 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2022 21, p 4129
allfieldsSound	10.3390/math10214129 doi (DE-627)DOAJ028680588 (DE-599)DOAJfc0ad0682e4c473cac2050ed4d65c3b1 DE-627 ger DE-627 rakwb eng QA1-939 Chengwei Yu verfasserin aut Regularity for Quasi-Linear <i<p</i<-Laplacian Type Non-Homogeneous Equations in the Heisenberg Group 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier When <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<2</mn<<mo<−</mo<<mn<1</mn<<mo</</mo<<mi<Q</mi<<mo<<</mo<<mi<p</mi<<mo<≤</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, we establish the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<0</mn<<mo<,</mo<<mn<1</mn<</mrow<</msubsup<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<1</mn<<mo<,</mo<<mi<α</mi<</mrow<</msubsup<</semantics<</math<</inline-formula<-regularities of weak solutions to quasi-linear <i<p</i<-Laplacian type non-homogeneous equations in the Heisenberg group <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mo<=</mo<<mn<2</mn<<mi<n</mi<<mo<+</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula< is the homogeneous dimension of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<. <i<p</i<-Laplacian type non-homogeneous equations Heisenberg group regularities Riesz potentials Mathematics In Mathematics MDPI AG, 2013 10(2022), 21, p 4129 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:10 year:2022 number:21, p 4129 https://doi.org/10.3390/math10214129 kostenfrei https://doaj.org/article/fc0ad0682e4c473cac2050ed4d65c3b1 kostenfrei https://www.mdpi.com/2227-7390/10/21/4129 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2022 21, p 4129
language	English
source	In Mathematics 10(2022), 21, p 4129 volume:10 year:2022 number:21, p 4129
sourceStr	In Mathematics 10(2022), 21, p 4129 volume:10 year:2022 number:21, p 4129
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	<i<p</i<-Laplacian type non-homogeneous equations Heisenberg group regularities Riesz potentials Mathematics
isfreeaccess_bool	true
container_title	Mathematics
authorswithroles_txt_mv	Chengwei Yu @@aut@@
publishDateDaySort_date	2022-01-01T00:00:00Z
hierarchy_top_id	737287764
id	DOAJ028680588
language_de	englisch
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callnumber-first	Q - Science
author	Chengwei Yu
spellingShingle	Chengwei Yu misc QA1-939 misc <i<p</i<-Laplacian type misc non-homogeneous equations misc Heisenberg group misc regularities misc Riesz potentials misc Mathematics Regularity for Quasi-Linear <i<p</i<-Laplacian Type Non-Homogeneous Equations in the Heisenberg Group
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topic_title	QA1-939 Regularity for Quasi-Linear <i<p</i<-Laplacian Type Non-Homogeneous Equations in the Heisenberg Group <i<p</i<-Laplacian type non-homogeneous equations Heisenberg group regularities Riesz potentials
topic	misc QA1-939 misc <i<p</i<-Laplacian type misc non-homogeneous equations misc Heisenberg group misc regularities misc Riesz potentials misc Mathematics
topic_unstemmed	misc QA1-939 misc <i<p</i<-Laplacian type misc non-homogeneous equations misc Heisenberg group misc regularities misc Riesz potentials misc Mathematics
topic_browse	misc QA1-939 misc <i<p</i<-Laplacian type misc non-homogeneous equations misc Heisenberg group misc regularities misc Riesz potentials misc Mathematics
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title	Regularity for Quasi-Linear <i<p</i<-Laplacian Type Non-Homogeneous Equations in the Heisenberg Group
ctrlnum	(DE-627)DOAJ028680588 (DE-599)DOAJfc0ad0682e4c473cac2050ed4d65c3b1
title_full	Regularity for Quasi-Linear <i<p</i<-Laplacian Type Non-Homogeneous Equations in the Heisenberg Group
author_sort	Chengwei Yu
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doi_str_mv	10.3390/math10214129
title_sort	regularity for quasi-linear <i<p</i<-laplacian type non-homogeneous equations in the heisenberg group
callnumber	QA1-939
title_auth	Regularity for Quasi-Linear <i<p</i<-Laplacian Type Non-Homogeneous Equations in the Heisenberg Group
abstract	When <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<2</mn<<mo<−</mo<<mn<1</mn<<mo</</mo<<mi<Q</mi<<mo<<</mo<<mi<p</mi<<mo<≤</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, we establish the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<0</mn<<mo<,</mo<<mn<1</mn<</mrow<</msubsup<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<1</mn<<mo<,</mo<<mi<α</mi<</mrow<</msubsup<</semantics<</math<</inline-formula<-regularities of weak solutions to quasi-linear <i<p</i<-Laplacian type non-homogeneous equations in the Heisenberg group <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mo<=</mo<<mn<2</mn<<mi<n</mi<<mo<+</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula< is the homogeneous dimension of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<.
abstractGer	When <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<2</mn<<mo<−</mo<<mn<1</mn<<mo</</mo<<mi<Q</mi<<mo<<</mo<<mi<p</mi<<mo<≤</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, we establish the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<0</mn<<mo<,</mo<<mn<1</mn<</mrow<</msubsup<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<1</mn<<mo<,</mo<<mi<α</mi<</mrow<</msubsup<</semantics<</math<</inline-formula<-regularities of weak solutions to quasi-linear <i<p</i<-Laplacian type non-homogeneous equations in the Heisenberg group <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mo<=</mo<<mn<2</mn<<mi<n</mi<<mo<+</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula< is the homogeneous dimension of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<.
abstract_unstemmed	When <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<2</mn<<mo<−</mo<<mn<1</mn<<mo</</mo<<mi<Q</mi<<mo<<</mo<<mi<p</mi<<mo<≤</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, we establish the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<0</mn<<mo<,</mo<<mn<1</mn<</mrow<</msubsup<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<1</mn<<mo<,</mo<<mi<α</mi<</mrow<</msubsup<</semantics<</math<</inline-formula<-regularities of weak solutions to quasi-linear <i<p</i<-Laplacian type non-homogeneous equations in the Heisenberg group <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mo<=</mo<<mn<2</mn<<mi<n</mi<<mo<+</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula< is the homogeneous dimension of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mrow<<mi mathvariant="double-struck"<H</mi<</mrow<<mi<n</mi<</msup<</semantics<</math<</inline-formula<.
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Regularity for Quasi-Linear <i<p</i<-Laplacian Type Non-Homogeneous Equations in the Heisenberg Group

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