Integral representation and Γ-convergence of variational integrals with p(x)-growth
Dipartimento di Matematica,
Università di Parma, via M. D'Azeglio 85/A, 43100 Parma, Italy; firstname.lastname@example.org.
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.
Mathematics Subject Classification: 49J45 / 49M20 / 46E35
Key words: Integral representation / Γ-convergence / nonstandard growth conditions.
© EDP Sciences, SMAI, 2002