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: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/950134 |
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| _version_ | 1849698009582927872 |
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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. |
| format | Article |
| id | doaj-art-aa7a951e42844fa4b741c7e1b552bc17 |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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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