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An integral representation result is obtained for the variational limit of the family of functionals \(\int _{\varOmega }f(\frac {x}{\varepsilon },D u)dx\), e > 0, when the integrand f = f(x, v) is a Caratheodory function, periodic in x, convex in v and with nonstandard growth.

Relaxation of Periodic and Nonstandard Growth Integrals by Means of Two-Scale Convergence