Integral representation and Γ-convergence of variational integrals withp(x)-growth
Alessandra Coscia, Domenico Mucci · ESAIM Control Optimisation and Calculus of Variations · 2002
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.