Optimal partial regularity of second-order parabolic systems under natural growth condition
1 School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian, 363000, China
2 School of Mathematical Science, Xiamen University, Xiamen, Fujian, 361005, China
Boundary Value Problems 2013, 2013:152 doi:10.1186/1687-2770-2013-152Published: 26 June 2013
We consider the regularity for weak solutions of second-order nonlinear parabolic systems under a natural growth condition when , 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.