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Everywhere regularity for vectorial functionals with general growth

Published online by Cambridge University Press:  15 September 2003

Elvira Mascolo  and
Anna Paola Migliorini
Elvira Mascolo
Affiliation:
Dipartimento di Matematica “U. Dini”, Universita' di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy; [email protected].
Anna Paola Migliorini
Affiliation:
Dipartimento di Matematica “U. Dini”, Universita' di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy; [email protected].
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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 $$ F\left(u \right)=\int_{\Omega}a(x)[h\left(|Du|\right)]^{p(x)}{\rm d}x $$ with h a convex function with general growth (also exponential behaviour is allowed).

Keywords

Minimizersregularitynonstandard growthexponential growth.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 9 , January 2003 , pp. 399 - 418
Copyright
© EDP Sciences, SMAI, 2003

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