Partial Regularity for Nonlinear Subelliptic Systems with Dini Continuous Coefficients in Heisenberg Groups

This paper is concerned with partial regularity to nonlinear subelliptic systems with Dini continuous coefficients under quadratic controllable growth conditions in the Heisenberg group ℍn. Based on a generalization of the technique of 𝒜-harmonic approximation introduced by Duzaar and Steffen, parti...

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Main Authors: Jialin Wang, Pingzhou Hong, Dongni Liao, Zefeng Yu
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/950134
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author Jialin Wang
Pingzhou Hong
Dongni Liao
Zefeng Yu
author_facet Jialin Wang
Pingzhou Hong
Dongni Liao
Zefeng Yu
author_sort Jialin Wang
collection DOAJ
description This paper is concerned with partial regularity to nonlinear subelliptic systems with Dini continuous coefficients under quadratic controllable growth conditions in the Heisenberg group ℍn. Based on a generalization of the technique of 𝒜-harmonic approximation introduced by Duzaar and Steffen, partial regularity to the sub-elliptic system is established in the Heisenberg group. Our result is optimal in the sense that in the case of Hölder continuous coefficients we establish the optimal Hölder exponent for the horizontal gradients of the weak solution on its regular set.
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issn 1085-3375
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language English
publishDate 2013-01-01
publisher Wiley
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series Abstract and Applied Analysis
spelling doaj-art-aa7a951e42844fa4b741c7e1b552bc172025-08-20T03:19:02ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/950134950134Partial Regularity for Nonlinear Subelliptic Systems with Dini Continuous Coefficients in Heisenberg GroupsJialin Wang0Pingzhou Hong1Dongni Liao2Zefeng Yu3School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, Jiangxi 341000, ChinaSchool of Mathematics and Computer Science, Gannan Normal University, Ganzhou, Jiangxi 341000, ChinaSchool of Mathematics and Computer Science, Gannan Normal University, Ganzhou, Jiangxi 341000, ChinaSchool of Mathematics and Computer Science, Gannan Normal University, Ganzhou, Jiangxi 341000, ChinaThis paper is concerned with partial regularity to nonlinear subelliptic systems with Dini continuous coefficients under quadratic controllable growth conditions in the Heisenberg group ℍn. Based on a generalization of the technique of 𝒜-harmonic approximation introduced by Duzaar and Steffen, partial regularity to the sub-elliptic system is established in the Heisenberg group. Our result is optimal in the sense that in the case of Hölder continuous coefficients we establish the optimal Hölder exponent for the horizontal gradients of the weak solution on its regular set.http://dx.doi.org/10.1155/2013/950134
spellingShingle Jialin Wang
Pingzhou Hong
Dongni Liao
Zefeng Yu
Partial Regularity for Nonlinear Subelliptic Systems with Dini Continuous Coefficients in Heisenberg Groups
Abstract and Applied Analysis
title Partial Regularity for Nonlinear Subelliptic Systems with Dini Continuous Coefficients in Heisenberg Groups
title_full Partial Regularity for Nonlinear Subelliptic Systems with Dini Continuous Coefficients in Heisenberg Groups
title_fullStr Partial Regularity for Nonlinear Subelliptic Systems with Dini Continuous Coefficients in Heisenberg Groups
title_full_unstemmed Partial Regularity for Nonlinear Subelliptic Systems with Dini Continuous Coefficients in Heisenberg Groups
title_short Partial Regularity for Nonlinear Subelliptic Systems with Dini Continuous Coefficients in Heisenberg Groups
title_sort partial regularity for nonlinear subelliptic systems with dini continuous coefficients in heisenberg groups
url http://dx.doi.org/10.1155/2013/950134
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AT pingzhouhong partialregularityfornonlinearsubellipticsystemswithdinicontinuouscoefficientsinheisenberggroups
AT dongniliao partialregularityfornonlinearsubellipticsystemswithdinicontinuouscoefficientsinheisenberggroups
AT zefengyu partialregularityfornonlinearsubellipticsystemswithdinicontinuouscoefficientsinheisenberggroups