Charles University in Prague, Faculty of Mathematics and Physics
Abstract
summary:In this paper we prove a regularity result for very weak solutions of equations of the type −divA(x,u,Du)=B(x,u,Du), where A, B grow in the gradient like tp−1 and B(x,u,Du) is not in divergence form. Namely we prove that a very weak solution u∈W1,r of our equation belongs to W1,p. We also prove global higher integrability for a very weak solution for the Dirichlet problem \cases -\operatorname{div} A(x,u,Du)\,=B(x, u,Du) \quad & \text{in } \Omega , \ u-u_o\in W^{1,r}(\Omega,\Bbb R^m). \endcases $