Partial Regularity of Solutions of Nonlinear Superelliptic Systems with Subquadratic Growth

Abstract

We prove global partial regularity of weak solutions $u$ of the Dirichlet problem for the nonlinear superelliptic system div $A(x,u,Du)+B(x,u,Du)=0$, under natural subquadratic polynomial growth of the coefficient functions $A$ and $B$. We employ the indirect method of the bilinear form and do not use a Caccioppoli or a reverse Hölder inequality.