Stochastic homogenization of degenerate integral functionals with linear growth

TL;DR

This paper investigates the homogenization process of non-convex, vectorial, random integral functionals with degenerate linear growth, showing convergence to a non-degenerate functional on BV under minimal assumptions.

Contribution

It introduces a novel homogenization result for degenerate integral functionals with linear growth, extending the theory to non-convex and random settings.

Findings

Homogenization of non-convex, random integral functionals with linear growth.

Convergence to a non-degenerate functional on BV.

Works under minimal assumptions on integrands and weight-functions.

Abstract

We study the limit behaviour of a sequence of non-convex, vectorial, random integral functionals, defined on $W^{1,1}$, whose integrands satisfy degenerate linear growth conditions. These involve suitable random, scale-dependent weight-functions. Under minimal assumptions on the integrand and on the weight-functions, we show that the sequence of functionals homogenizes to a non-degenerate functional defined on $BV$.