Partial Regularity for Nonlinear Subelliptic Systems with Dini Continuous Coefficients in Heisenberg Groups
This article is part of Special Issue:
Jialin Wang,
Pingzhou Hong,
Dongni Liao,
Zefeng Yu,
Corresponding Author
Jialin Wang
School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, Jiangxi 341000, China gnnu.cn
Search for more papers by this authorPingzhou Hong
School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, Jiangxi 341000, China gnnu.cn
Search for more papers by this authorDongni Liao
School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, Jiangxi 341000, China gnnu.cn
Search for more papers by this authorZefeng Yu
School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, Jiangxi 341000, China gnnu.cn
Search for more papers by this authorJialin Wang,
Pingzhou Hong,
Dongni Liao,
Zefeng Yu,
Corresponding Author
Jialin Wang
School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, Jiangxi 341000, China gnnu.cn
Search for more papers by this authorPingzhou Hong
School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, Jiangxi 341000, China gnnu.cn
Search for more papers by this authorDongni Liao
School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, Jiangxi 341000, China gnnu.cn
Search for more papers by this authorZefeng Yu
School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, Jiangxi 341000, China gnnu.cn
Search for more papers by this authorFirst published: 02 October 2013
Academic Editor: Pekka Koskela
Abstract
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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