Boundary regularity result for quasilinear elliptic systems
1 Department of Mathematics and Information Science, Zhangzhou Normal University, Zhangzhou 363000, Fujian, China
2 School of Mathematical Science, Xiamen University, Xiamen 361005, Fujian, China
Journal of Inequalities and Applications 2012, 2012:102 doi:10.1186/1029-242X-2012-102Published: 30 April 2012
We consider boundary regularity for weak solutions of second-order quasilinear elliptic systems under controllable growth condition, and obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. Combined with existing results on interior partial regularity, this result yields an upper bound on the Hausdorff dimension of the singular set at the boundary.