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arXiv · 1712.07272

Stochastic Homogenisation of Free-Discontinuity Problems

Filippo Cagnetti·Gianni Dal Maso·Lucia Scardia·Caterina Ida Zeppieri
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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.

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Filippo Cagnetti, Gianni Dal Maso, Lucia Scardia, Caterina Ida Zeppieri. 2017-12-20. Stochastic Homogenisation of Free-Discontinuity Problems. https://arxiv.org/abs/1712.07272

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