Calculus of Variations and Geometric Measure Theory

A. Bach - M. Ruf

Fluctuation estimates for the multi-cell formula in stochastic homogenization of partitions

created by ruf on 18 Mar 2021
modified on 31 Jan 2022


Accepted Paper

Inserted: 18 mar 2021
Last Updated: 31 jan 2022

Journal: Calc. Var. Partial Differential Equations
Year: 2022

ArXiv: 2105.13846 PDF


In this paper we derive quantitative estimates in the context of stochastic homogenization for integral functionals defined on finite partitions, where the random surface integrand is assumed to be stationary. Requiring the integrand to satisfy in addition a multiscale functional inequality, we control quantitatively the fluctuations of the asymptotic cell formulas defining the homogenized surface integrand. As a byproduct we obtain a simplified cell formula where we replace cubes by almost flat hyperrectangles.