Calculus of Variations and Geometric Measure Theory
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A. Passarelli di Napoli

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

created by passarell on 22 Apr 2013

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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.


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