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Boundary regularity for quasilinear elliptic systems with super quadratic controllable 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 2014, 2014:88  doi:10.1186/1687-2770-2014-88

Published: 6 May 2014


We consider the boundary regularity for weak solutions to quasilinear elliptic systems under a super quadratic controllable growth condition, and we obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. Combined with existing results on the interior partial regularity, this result yields an upper bound on the Hausdorff dimension of a singular set at the boundary.

quasilinear elliptic systems; controllable growth condition; A-harmonic approximation technique; boundary partial regularity