Calculus of Variations and Geometric Measure Theory
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E. Acerbi - G. Mingione

Gradient Estimates for the p(x)-Laplacean System

created on 06 May 2004
modified by mingione on 30 Oct 2005

[BibTeX]

Published Paper

Inserted: 6 may 2004
Last Updated: 30 oct 2005

Journal: J. Reine Angew. Math. (Crelle J.)
Volume: 584
Pages: 117-148
Year: 2005

Abstract:

We prove Calderón-Zygmund type estimates for a class of elliptic problems whose model is the non-homogeneous $p(x)$-Laplacean system: $$ div (
Du
{p(x)-2}Du) = div (
F
{p(x)-2}F)\:.$$ In particular, under optimal continuity assumptions on the exponent function $p(x)>1$ we prove that $$
F
{p(x)} in Lq{loc} \ \ \ \mbox{implies}\ \ \
Du
{p(x)} in Lq{loc}\ \ \ \ \mbox{for every}\ \ q>1\:.$$ This extends to the non linear setting estimates by Diening & Ruzicka (Crelle J. 2003).

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