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.
2009
34
1607
1631
M.Focardi
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/333770
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