First-order expansion of homogenized coefficients under Bernoulli perturbations

2013/01/31 by Jean-Christophe Mourrat, Mourrat, Jean-Christophe
Computer Science · Engineering · Mathematics · #35B27 #35J15 #35R60 #82D30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical methods in inverse problems #Probability (math.PR) #math.AP #math.PR #msc:35B27 #msc:35J15 #msc:35R60 #msc:82D30

paper · pdf · doi:10.48550/arxiv.1301.7685

32 pages. V3: revised introduction, some corrections and clarifications

openalex publication_date 2013/01/31 · arxiv created 2013/11/19 · arxiv updated 2013/11/20 · openalex created_date 2025/10/27 · openalex updated_date 2026/08/04

Abstract

Divergence-form operators with stationary random coefficients homogenize over large scales. We investigate the effect of certain perturbations of the medium on the homogenized coefficients. The perturbations that we consider are rare at the local level, but when occurring, have an effect of the same order of magnitude as the initial medium itself. The main result of the paper is a first-order expansion of the homogenized coefficients, as a function of the perturbation parameter.

Citations

• Elements of mathematical foundations for a numerical approach for weakly random homogenization problems
• Random walks on supercritical percolation clusters

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