Calculus of Variations and Geometric Measure Theory

F. Cagnetti - G. Dal Maso - L. Scardia - C. I. Zeppieri

A global method for deterministic and stochastic homogenisation in BV

created by dalmaso on 19 Jan 2021
modified on 11 Jul 2023


Published Paper

Inserted: 19 jan 2021
Last Updated: 11 jul 2023

Journal: Ann. PDE
Volume: 8
Number: 1
Pages: Paper No. 8
Year: 2022


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.