Calculus of Variations and Geometric Measure Theory

M. Ruf - C. I. Zeppieri

Stochastic homogenization of degenerate integral functionals with linear growth

created by zeppieri1 on 26 Oct 2022
modified on 15 Nov 2022


Submitted Paper

Inserted: 26 oct 2022
Last Updated: 15 nov 2022

Year: 2022


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 $BV$.

Keywords: $\Gamma$-convergence, $BV$ functions, stochastic homogenization, vectorial integral functionals, degenerate linear growth