Homogenization of Random Fractional Obstacle Problems via Γ-convergence

Γ-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 in [8], a weighted ergodic theorem and a joining lemma in varying domains following the approach by [1]. Our proof is alternative to those contained in [6], [7]. 2000 Mathematics Subject Classification: 35B27, 49J45.