Boundary regularity for quasilinear elliptic systems with super quadratic controllable growth condition

摘要

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.