Relaxation of Periodic and Nonstandard Growth Integrals by means of Two-scale convergence

Abstract

An integral representation result is obtained for the variational limit of the family functionals ${\int }_{\Omega }f\left(\frac{x}{\epsilon },Du\right)dx$, as $\epsilon \to 0$, when the integrand $f=f(x,v)$ is a Carathéodory function, periodic in $x$, convex in $v$ and with nonstandard growth.