Optimal interior partial regularity for nonlinear elliptic systems

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August 2010, 27(3): 981-993. doi: 10.3934/dcds.2010.27.981

Optimal interior partial regularity for nonlinear elliptic systems

1.	Department of Information and Mathematics Sciences, China Jiliang University, Hangzhou 310018, Zhejiang, China
2.	School of Mathematical Science, Xiamen University, Xiamen 361005, Fujian, China

Received December 2008 Revised February 2010 Published March 2010

Abstract
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We consider interior regularity for weak solutions of nonlinear elliptic systems with subquadratic under controllable growth condition. By $\mathcal{A}$-harmonic approximation technique, we obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particularly, the regular result is optimal.

Keywords: Controllable growth condition, Nonlinear elliptic systems, Optimal partial regularity., $\mathcal{A}$-harmonic approximation technique.

Mathematics Subject Classification: Primary: 35J15, 35J60; Secondary: 42B3.

Citation: Shuhong Chen, Zhong Tan. Optimal interior partial regularity for nonlinear elliptic systems. Discrete & Continuous Dynamical Systems - A, 2010, 27 (3) : 981-993. doi: 10.3934/dcds.2010.27.981

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