Optimal interior partial regularity for nonlinear ellipticsystems

Shuhong Chen; Zhong Tan

doi:10.3934/dcds.2010.27.981

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2010, Volume 27, Issue 3: 981-993. Doi: 10.3934/dcds.2010.27.981

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Optimal interior partial regularity for nonlinear elliptic systems

Shuhong Chen^1, and
Zhong Tan^2,

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

Received: November 30, 2008

Revised: January 31, 2010

Published: August 2010

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Abstract

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:

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

Mathematics Subject Classification: Primary: 35J15, 35J60; Secondary: 42B37.

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