Partial regularity up to the boundary for solutions of subquadratic elliptic systems

Advances in Nonlinear Analysis

article

Zhong Tan¹  Yanzhen Wang²  Shuhong Chen³ 

[1] School of Mathematical Science and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University;School of Mathematical Sciences, Xiamen University;School of Mathematics and Statistics, Minnan Normal University

关键词: Subquadratic elliptic systems;    controllable growth condition;    higher integrability;    partial regularity;   

DOI  :  10.1515/anona-2016-0054

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In this paper, we are concerned with the nonlinear elliptic systems in divergence form under controllable growth condition. We prove that the weak solution u is locally Hölder continuous besides a singular set by using the direct method and classical Morrey-type estimates. Here the Hausdorff dimension of the singular set is less than n-p{n-p}. This result not only holds in the interior, but also holds up to the boundary.

【 授权许可】

CC BY