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