Published Paper

Inserted: 15 sep 2021
Last Updated: 13 jul 2023

Journal: Proc. Roy. Soc. Edinburgh Section A
Volume: 153
Number: 2
Pages: 491--544
Year: 2023

Abstract:

We study the $\Gamma$-convergence of nonconvex vectorial integral functionals whose integrands satisfy possibly degenerate growth and coercivity conditions. The latter involve suitable scale-dependent weight functions. We prove that under appropriate uniform integrability conditions on the weight functions, which shall belong to a Muckenhoupt class, the corresponding functionals $\Gamma$-converge, up to subsequences, to a degenerate integral functional defined on a limit weighted Sobolev space.

The general analysis is then applied to the case of random stationary integrands and weights to prove a stochastic homogenisation result for the corresponding functionals.

Keywords: $\Gamma$-convergence, weighted Sobolev spaces, Muckenhoupt weights, stochastic homogenisation, degenerate growth conditions

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