A global method for deterministic and stochastic homogenisation in BV

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

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we study the deterministic and stochastic homogenisation of free-discontinuity functionals under linear growth and coercivity conditions. The main novelty of our deterministic result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Combining this result with the pointwise Subadditive Ergodic Theorem by Akcoglu and Krengel, we prove a stochastic homogenisation result, in the case of stationary random integrands. In particular, we characterise the limit integrands in terms of asymptotic cell formulas, as in the classical case of periodic homogenisation.

Original languageEnglish
Article number8
JournalAnnals of PDE
Volume8
Issue number1
Early online date7 Apr 2022
DOIs
Publication statusE-pub ahead of print - 7 Apr 2022

Keywords

  • Blow-up method
  • Free-discontinuity problems
  • Stochastic homogenisation
  • Γ -convergence

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Geometry and Topology
  • Mathematical Physics
  • Physics and Astronomy(all)

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