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Existence and regularity of minimizers of nonconvex integrals with p-q growth

Published online by Cambridge University Press:  12 May 2007

Pietro Celada ,
Giovanni Cupini  and
Marcello Guidorzi
Pietro Celada
Affiliation:
Dipartimento di Matematica – Università degli Studi di Parma, Parco Area delle Scienze 53/A, 43100 Parma, Italy; [email protected]
Giovanni Cupini
Affiliation:
Dipartimento di Matematica “U. Dini” – Università degli Studi di Firenze, V. le Morgagni 67/A, 50134 Firenze Italy; [email protected]
Marcello Guidorzi
Affiliation:
Dipartimento di Matematica – Università degli Studi di Ferrara, Via Machiavelli 35, 44100 Ferrara, Italy; [email protected]
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Abstract

We show that local minimizers of functionals of the form $\int_{\Omega} \left[f(Du(x)) + g(x\,,u(x))\right]\,{\rm d}x$ ,  $u \in u_0 + W_0^{1,p}(\Omega)$ ,are locally Lipschitz continuous provided f is a convex function with $p-q$ growth satisfying a condition of qualified convexity at infinity and g is Lipschitz continuous in u. As a consequence of this, we obtain an existence result for a related nonconvex functional.

Keywords

Nonstandard growthexistenceLipschitz continuity
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 2 , April 2007 , pp. 343 - 358
Copyright
© EDP Sciences, SMAI, 2007

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