Γ-convergence and stochastic homogenization of degenerate integral functionals in weighted Sobolev spaces. Issue 2 (April 2023)

• Record Type: Journal Article
• Authors: D'Onofrio, Chiara; Zeppieri, Caterina Ida
• Is Part Of: Proceedings. Volume 153:Issue 2(2023)
• Page Start: 491
• Page End: 544
• Publication Date: 2023-04
• Subjects: Γ-convergence -- degenerate growth conditions -- Muckenhoupt weights -- weighted Sobolev spaces -- stochastic homogenization; 49J45 -- 35J70 -- 74B20 -- 74G65 -- 74Q05; Mathematics -- Periodicals; 510
• DOI: 10.1017/prm.2022.3
• Languages: English
• ISSNs: 0308-2105

Abstract

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 homogenization result for the corresponding functionals.