Calculus of Variations and Geometric Measure Theory

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

Stochastic Homogenisation of Free-Discontinuity Problems

created by cagnetti on 20 Dec 2017
modified by dalmaso on 04 Jul 2022


Published Paper

Inserted: 20 dec 2017
Last Updated: 4 jul 2022

Journal: Arch. Ration. Mech. Anal.
Volume: 233
Pages: 935-974
Year: 2019


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.