Inserted: 22 apr 2013
Last Updated: 22 apr 2013
We establish higher differentiability results for local solutions of elliptic systems of the type $$\div A(x,Du)=0 $$ in a bounded open set in $ \R^2$. The operator $A(x,\xi)$ is assumed to be strictly monotone and Lipschitz continuous with respect to variable $\xi$. The novelty of the paper is that we allow discontinuous dependence with respect to the $x$-variable, through a suitable Sobolev function.