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

Author:

Tan Zhong1,Wang Yanzhen2,Chen Shuhong3

Affiliation:

1. School of Mathematical Science and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen, Fujian, 361005, P. R. China

2. School of Mathematical Sciences, Xiamen University, Xiamen, Fujian, 361005, P. R. China

3. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian, 363000, P. R. China

Abstract

AbstractIn 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}. This result not only holds in the interior, but also holds up to the boundary.

Funder

National Natural Science Foundation of China

Publisher

Walter de Gruyter GmbH

Subject

Analysis

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