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Stochastic homogenisation of free-discontinuity problems

Version 2 2023-06-12, 09:02
Version 1 2023-06-09, 17:07
journal contribution
posted on 2023-06-12, 09:02 authored by Filippo Cagnetti, Gianni Dal Maso, Lucia Scardia, Caterina Ida Zeppieri
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.

Funding

Symmetry of Minimisers in Calculus of Variations; G2048; EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL; EP/P007287/1

History

Publication status

  • Published

File Version

  • Published version

Journal

Archive for Rational Mechanics and Analysis

ISSN

0003-9527

Publisher

Springer Verlag

Issue

240

Volume

233

Page range

935-974

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Analysis and Partial Differential Equations Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2019-03-07

First Open Access (FOA) Date

2019-04-09

First Compliant Deposit (FCD) Date

2019-03-06

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