Calculus of Variations and Geometric Measure Theory
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A. Coscia - G. Mingione

Hölder continuity of the gradient of $p(x)$-harmonic mappings

created on 01 Feb 2002
modified on 06 Jul 2002

[BibTeX]

Published Paper

Inserted: 1 feb 2002
Last Updated: 6 jul 2002

Journal: C. R. Acad. Sci. Paris Sér. I Math.
Volume: 328
Number: 4
Pages: 363-368
Year: 1999

Abstract:

Consider the following functional: $$ \int
Du
{p(x)}\ dx $$ where: $u:\Omega \to R^N$. We prove that if $u$ is a minimizer then $Du$ is locally Hölder continuous provided $p(x)>1$ is locally Hölder. This result is, of course, sharp.

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