Open Access Research Article

Optimal Interior Partial Regularity for Nonlinear Elliptic Systems for the Case under Natural Growth Condition

Shuhong Chen1,2* and Zhong Tan2

Author Affiliations

1 Department of Information and Mathematics Sciences, China Jiliang University, Hangzhou, Zhejiang 310018, China

2 School of Mathematical Science, Xiamen University, Xiamen, Fujian 361005, China

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Journal of Inequalities and Applications 2010, 2010:680714 doi:10.1155/2010/680714

Published: 6 April 2010

Abstract

We consider the interior regularity for weak solutions of second-order nonlinear elliptic systems with subquadratic growth under natural growth condition. We obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particularly the regularity we obtained is optimal.