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MiS Preprint
21/1998
Homogenization of periodic multi-dimensional structures
Nadia Ansini, Andrea Braides and Valeria Chiadò Piat
Abstract
We study the asymptotic behaviour of a class of oscillating integral functionals, which may depend on measures concentrated on periodic low-dimensional or multi-dimensional structures. We set the problem in the framework of Sobolev spaces with respect to periodic measures, and show that, under proper assumptions, a limit functional defined on the usual Sobolev space can be obtained using the techniques of $\Gamma$-convergence, whose energy density is described by an appropriate formula.