Partial regularity of solutions of nonlinear superelliptic systems with subquadratic growth (Q2418829)

Summary: 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.