Stochastic homogenisation of free-discontinuity problems

Cagnetti, Filippo, Dal Maso, Gianni, Scardia, Lucia and Ida Zeppieri, Caterina (2019) Stochastic homogenisation of free-discontinuity problems. Archive for Rational Mechanics and Analysis, 233 (240). pp. 935-974. ISSN 0003-9527

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Abstract

In this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which is deterministic in the ergodic case. Moreover, by establishing a connection between the deterministic convergence of the functionals at any fixed realisation and the pointwise Subadditive Ergodic Theorem by Akcoglou and Krengel, we characterise the limit volume and surface integrands in terms of asymptotic cell formulas.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Analysis and Partial Differential Equations Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Alice Jackson
Date Deposited: 07 Mar 2019 10:43
Last Modified: 05 Jul 2019 15:15
URI: http://sro.sussex.ac.uk/id/eprint/82312

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Project NameSussex Project NumberFunderFunder Ref
Symmetry of Minimisers in Calculus of VariationsG2048EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCILEP/P007287/1