We consider boundary regularity for weak solutions of second-order quasilinear elliptic systems under natural growth condition with super quadratic growth 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.
"Regularity Result for Quasilinear Elliptic Systems with Super Quadratic Natural Growth Condition." Abstr. Appl. Anal. 2013 1 - 8, 2013. https://doi.org/10.1155/2013/676215