WIAS Preprint No. 2932, (2022)

Stochastic homogenization on perforated domains III -- General estimates for stationary ergodic random connected Lipschitz domains


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

2020 Mathematics Subject Classification

  • 80M40 60D05




This is Part III of a series on the existence of uniformly bounded extension operators on randomly perforated domains in the context of homogenization theory. Recalling that randomly perforated domains are typically not John and hence extension is possible only from W 1,p to W 1,r, r < p, we will show that the existence of such extension operators can be guarantied if the weighted expectations of four geometric characterizing parameters are bounded: The local Lipschitz constant M, the local Lipschitz radius Δ , the mesoscopic Voronoi diameter ∂ and the local connectivity radius R.

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