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Open Access Research

Optimal partial regularity of second-order parabolic systems under natural growth condition

Shuhong Chen1 and Zhong Tan2*

Author Affiliations

1 School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian, 363000, China

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

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Boundary Value Problems 2013, 2013:152  doi:10.1186/1687-2770-2013-152

Published: 26 June 2013

Abstract

We consider the regularity for weak solutions of second-order nonlinear parabolic systems under a natural growth condition when <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/152/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/152/mathml/M1">View MathML</a>, and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particular, we get the optimal regularity by the method of A-caloric approximation introduced by Duzaar and Mingione.

Keywords:
nonlinear parabolic systems; natural growth condition; A-caloric approximation; optimal partial regularity