Everywhere regularity for vectorial functionals with general growth

Free access article

Issue		ESAIM: COCV Volume 9, 2003


Page(s)		399 - 418
DOI		10.1051/cocv:2003019

ESAIM: COCV, May 2003, Vol. 9, pp. 399-418
DOI: 10.1051/cocv:2003019

Everywhere regularity for vectorial functionals with general growth

Elvira Mascolo and Anna Paola Migliorini

Dipartimento di Matematica "U. Dini", Universita' di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy; mascolo@math.unifi.it.

(Received September 4, 2001.)

Abstract
We prove Lipschitz continuity for local minimizers of integral functionals of the Calculus of Variations in the vectorial case, where the energy density depends explicitly on the space variables and has general growth with respect to the gradient. One of the models is

$\begin{displaymath}F\left(u \right)=\int_{\Omega}a(x)[h\left(\vert Du\vert\right)]^{p(x)}{\rm d}x \end{displaymath}$

with h a convex function with general growth (also exponential behaviour is allowed).

Mathematics Subject Classification. 49N60, 35J50.

Key words: Minimizers, regularity, nonstandard growth, exponential growth.

© EDP Sciences, SMAI 2003

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