## ESAIM: Control, Optimisation and Calculus of Variations

### Integral representation and Γ-convergence of variational integrals with p(x)-growth

a1 Dipartimento di Matematica, Università di Parma, via M. D'Azeglio 85/A, 43100 Parma, Italy; domenico.mucci@unipr.it.

Abstract

We study the integral representation properties of limits of sequences of integral functionals like     under nonstandard growth conditions of (p,q)-type: namely, we assume that Under weak assumptions on the continuous function p(x), we prove Γ-convergence to integral functionals of the same type. We also analyse the case of integrands f(x,u,Du) depending explicitly on u; finally we weaken the assumption allowing p(x) to be discontinuous on nice sets.

(Online publication September 15 2002)

Key Words:

• Integral representation;
• Γ-convergence;
• nonstandard growth conditions.

Mathematics Subject Classification:

• 49J45;
• 49M20;
• 46E35