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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; mascolo@math.unifi.it.
Anna Paola Migliorini
Affiliation:
Dipartimento di Matematica “U. Dini”, Universita' di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy; mascolo@math.unifi.it.
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Abstract

We prove Lipschitz continuity for localminimizers of integral functionals of the Calculus of Variationsin the vectorial case, where the energy density depends explicitlyon the space variables and has general growth with respect to thegradient. 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 behaviouris allowed).

Keywords

Minimizersregularitynonstandard growthexponential growth.

Information

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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