WIAS Preprint No. 2865, (2021)

Stochastic homogenization on perforated domains II -- Application to nonlinear elasticity models


  • Heida, Martin
    ORCID: 0000-0002-7242-8175

2020 Mathematics Subject Classification

  • 54E45 60D05 74Qxx 76M50 80M40


  • Homogenization, stochastic geometry, elasticity




Based on a recent work that exposed the lack of uniformly bounded W1,p → W1,p extension operators on randomly perforated domains, we study stochastic homogenization of nonlinear elasticity on such structures using instead the extension operators constructed in [11]. We thereby introduce two-scale convergence methods on such random domains under the intrinsic loss of regularity and prove some generally useful calculus theorems on the probability space Ω, e.g. abstract Gauss theorems.

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