Homogenization of unbounded integrals with quasiconvex growth

TL;DR

This paper investigates the homogenization process of certain nonconvex integrals with quasiconvex growth, using b3-convergence, to understand their effective behavior in periodic settings.

Contribution

It introduces a novel approach to homogenize unbounded integrals with quasiconvex growth and convex effective domain via b3-convergence.

Findings

Established homogenization results for unbounded integrals with quasiconvex growth.

Extended b3-convergence techniques to nonconvex integrals.

Provided conditions under which homogenization holds for these integrals.

Abstract

We study homogenization by $\Gamma$-convergence of periodic nonconvex integrals when the integrand has quasiconvex growth with convex effective domain.