Abstract and Applied Analysis
Volume 2013 (2013), Article ID 676215, 8 pages
http://dx.doi.org/10.1155/2013/676215
Research Article

Regularity Result for Quasilinear Elliptic Systems with Super Quadratic Natural Growth Condition

Shuhong Chen1 and Zhong Tan2

1Department of Mathematics and Information Science, Zhangzhou Normal University, Zhangzhou, Fujian 363000, China
2School of Mathematical Science, Xiamen University, Xiamen, Fujian 361005, China

Received 31 December 2012; Accepted 2 April 2013

Academic Editor: Paul Eloe

Copyright © 2013 Shuhong Chen and Zhong Tan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider boundary regularity for weak solutions of second-order quasilinear elliptic systems under natural growth condition with super quadratic growth and obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. Combined with existing results on interior partial regularity, this result yields an upper bound on the Hausdorff dimension of the singular set at the boundary.