Homogenization of random fractional obstacle problems via $Γ$-convergence

Details Homogenization of random fractional obstacle problems via $Γ$-convergence Homogenization of random fractional obstacle problems via $Γ$-convergence

2009-02-16

arxiv.org/abs/0902.2683v1

Mathematics

Classical Analysis and ODEs

Scientific paper

$\Gamma$-convergence methods are used to prove homogenization results for fractional obstacle problems in periodically perforated domains. The obstacles have random sizes and shapes and their capacity scales according to a stationary ergodic process. We use a trace-like representation of fractional Sobolev norms in terms of weighted Sobolev energies established by Caffarelli and Silvestre, a weighted ergodic theorem and a joining lemma in varying domains following the approach by Ansini and Braides. Our proof is alternative to those contained in the papers by Caffarelli and Mellet.

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