Optimal interior partial regularity for nonlinear elliptic systems for the case 1 < m < 2 under natural growth condition

Abstract

We consider the interior regularity for weak solutions of second-order nonlinear elliptic systems with subquadratic growth under natural growth condition. We obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particularly the regularity we obtained is optimal. Copyright © 2010 S. Chen and Z. Tan.