WIAS Preprint No. 2932, (2022)
Stochastic homogenization on perforated domains III -- General estimates for stationary ergodic random connected Lipschitz domains
Authors
- Heida, Martin
ORCID: 0000-0002-7242-8175
2020 Mathematics Subject Classification
- 80M40 60D05
DOI
Abstract
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.
Appeared in
- Netw. Heterog. Media, 18 (2023), pp. 1410--1433, DOI 10.3934/nhm.2023062 .
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