# Higher differentiability of solutions of elliptic systems with Sobolev coefficients: the case p=n=2

created by passarell on 22 Apr 2013

[BibTeX]

Submitted Paper

Inserted: 22 apr 2013
Last Updated: 22 apr 2013

Year: 2013

Abstract:

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.