Stochastic homogenisation of free-discontinuity problems

Filippo Cagnetti, Gianni Dal Maso, Lucia Scardia, Caterina Ida Zeppieri

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.
Original languageEnglish
Pages (from-to)935–974
Number of pages40
JournalArchive for Rational Mechanics and Analysis
Volume233
Issue number2
Early online date28 Mar 2019
DOIs
Publication statusPublished - 1 Aug 2019

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

Stochastic homogenisation of free-discontinuity problems. / Cagnetti, Filippo; Dal Maso, Gianni; Scardia, Lucia; Zeppieri, Caterina Ida.

In: Archive for Rational Mechanics and Analysis, Vol. 233, No. 2, 01.08.2019, p. 935–974.

Research output: Contribution to journalArticle

Cagnetti, F, Dal Maso, G, Scardia, L & Zeppieri, CI 2019, 'Stochastic homogenisation of free-discontinuity problems', Archive for Rational Mechanics and Analysis, vol. 233, no. 2, pp. 935–974. https://doi.org/10.1007/s00205-019-01372-x
Cagnetti, Filippo ; Dal Maso, Gianni ; Scardia, Lucia ; Zeppieri, Caterina Ida. / Stochastic homogenisation of free-discontinuity problems. In: Archive for Rational Mechanics and Analysis. 2019 ; Vol. 233, No. 2. pp. 935–974.
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