A global method for deterministic and stochastic homogenisation in BV

Cagnetti, Filippo, Dal Maso, Gianni, Scardia, Lucia and Zeppieri, Caterina Ida (2022) A global method for deterministic and stochastic homogenisation in BV. Annals of PDE, 8 (1). a8 1-89. ISSN 2524-5317

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Analysis and Partial Differential Equations Research Group
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 06 Apr 2022 08:30
Last Modified: 12 Apr 2022 12:00
URI: http://sro.sussex.ac.uk/id/eprint/105207

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