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Stochastic homogenisation of free-discontinuity problems
journal contribution
posted on 2023-06-12, 09:02 authored by Filippo Cagnetti, Gianni Dal Maso, Lucia Scardia, Caterina Ida ZeppieriIn 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 AnalysisISSN
0003-9527Publisher
Springer VerlagExternal DOI
Issue
240Volume
233Page range
935-974Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Analysis and Partial Differential Equations Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes