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

Regularity results for a class of functionals with nonstandard growth

created on 30 Nov 2001
modified on 06 Jul 2002

[BibTeX]

Published Paper

Inserted: 30 nov 2001
Last Updated: 6 jul 2002

Journal: Arch. Ration. Mech. Anal.
Volume: 156
Number: 2
Pages: 121-140
Year: 2001

Abstract:

We consider the integral functional $\int f(x,Du)\,dx$ under non standard growth assumptions that we call of $p(x)$ type: namely, we assume that $$
z
{p(x)}\le f(x,z)\le L(1+
z
{p(x)})\;,$$ a relevant model case being the functional $$\int
Du
{p(x)}\,dx\;.$$ Under sharp assumptions on the continuous function $p(x)>1$ we prove regularity of minimizers. Energies exhibiting this growth appear in several models from mathematical physics.

Keywords: regularity, integral functionals, Nonstandard growth, Minimizers

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