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 & Silvestre, a weighted ergodic theorem and a joining lemma in varying domains following the approach by Ansini & Braides. Our proof is alternative to those proposed by Caffarelli & Mellet.
Homogenization of random fractional obstacle problems via Gamma-convergence / M.Focardi. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - STAMPA. - 34:(2009), pp. 1607-1631. [10.1080/03605300903300728]
Homogenization of random fractional obstacle problems via Gamma-convergence
FOCARDI, MATTEO
2009
Abstract
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 & Silvestre, a weighted ergodic theorem and a joining lemma in varying domains following the approach by Ansini & Braides. Our proof is alternative to those proposed by Caffarelli & Mellet.File | Dimensione | Formato | |
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