{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,6,7]],"date-time":"2023-06-07T04:21:25Z","timestamp":1686111685501},"reference-count":11,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["NHM"],"published-print":{"date-parts":[[2023]]},"abstract":"<jats:p xml:lang=\"fr\">&lt;abstract&gt;&lt;p&gt;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 &amp;lt; p $, we will show that the existence of such extension operators can be guaranteed if the weighted expectations of four geometric characterizing parameters are bounded: The local Lipschitz constant $ M $, the local inverse Lipschitz radius $ \\delta^{-1} $ resp. $ \\rho^{-1} $, the mesoscopic Voronoi diameter $ {\\mathfrak{d}} $ and the local connectivity radius $ {\\mathscr{R}} $.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/nhm.2023062","type":"journal-article","created":{"date-parts":[[2023,6,6]],"date-time":"2023-06-06T17:27:50Z","timestamp":1686072470000},"page":"1410-1433","source":"Crossref","is-referenced-by-count":0,"title":["Stochastic homogenization on perforated domains III\u2013General estimates for stationary ergodic random connected Lipschitz domains"],"prefix":"10.3934","volume":"18","author":[{"given":"Martin","family":"Heida","sequence":"first","affiliation":[]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2023062-1","unstructured":"D. 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Heida, Stochastic homogenization on perforated domains I: Extension operators, arXiv: 2105.10945, [Preprint], (2021) [cited 2023 June 06 ]. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/arXiv.org\/abs\/2105.10945\">https:\/\/arXiv.org\/abs\/2105.10945<\/ext-link>"},{"key":"key-10.3934\/nhm.2023062-6","doi-asserted-by":"crossref","unstructured":"M. Heida, Stochastic homogenization on perforated domains II\u2013application to nonlinear elasticity models, <i>Z Angew Math Mech<\/i>, <b>102<\/b> (2022), e202100407.","DOI":"10.1002\/zamm.202100407"},{"key":"key-10.3934\/nhm.2023062-7","unstructured":"M. H\u00f6pker, Extension Operators for Sobolev Spaces on Periodic Domains, Their Applications, and Homogenization of a Phase Field Model for Phase Transitions in Porous Media, (German), Doctoral Thesis of University Bremen, Bremen, 2016."},{"key":"key-10.3934\/nhm.2023062-8","doi-asserted-by":"publisher","unstructured":"P. W. Jones, Quasiconformal mappings and extendability of functions in sobolev spaces, <i>Acta Math.<\/i>, <b>147<\/b> (1981), 71\u201388. https:\/\/doi.org\/10.1007\/BF02392869","DOI":"10.1007\/BF02392869"},{"key":"key-10.3934\/nhm.2023062-9","doi-asserted-by":"publisher","unstructured":"J. Mecke, Station\u00e4re zuf\u00e4llige Ma\u00dfe auf lokalkompakten abelschen Gruppen, <i>Probab Theory Relat<\/i>, <b>9<\/b> (1967), 36\u201358. https:\/\/doi.org\/10.1007\/BF00535466","DOI":"10.1007\/BF00535466"},{"key":"key-10.3934\/nhm.2023062-10","doi-asserted-by":"publisher","unstructured":"A. Piatnitski, M. 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Tempel'man, Ergodic theorems for general dynamical systems, <i>Trudy Moskovskogo Matematicheskogo Obshchestva<\/i>, <b>26<\/b> (1972), 95\u2013132."}],"container-title":["Networks and Heterogeneous Media"],"original-title":[],"link":[{"URL":"http:\/\/www.aimspress.com\/article\/doi\/10.3934\/nhm.2023062?viewType=html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,6]],"date-time":"2023-06-06T17:28:09Z","timestamp":1686072489000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.aimspress.com\/article\/doi\/10.3934\/nhm.2023062"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"references-count":11,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023]]}},"URL":"https:\/\/doi.org\/10.3934\/nhm.2023062","relation":{},"ISSN":["1556-1801"],"issn-type":[{"value":"1556-1801","type":"print"}],"subject":[],"published":{"date-parts":[[2023]]}}}