| Abstract: |
| We study the asymptotic behavior of fractional Dirichlet energies in periodically perforated domains via De Giorgi's Gamma-convergence. In the critical regime, we identify the so-called strange term in the spirit of Cioranescu and Murat. The proof relies on a mesoscopic annular freezing procedure, localized fractional capacitary estimates, and a bulk decoupling argument controlling the nonlocal interactions. We also characterize the subcritical and supercritical regimes: in the former the perforations are asymptotically invisible, while in the latter bounded-energy sequences collapse to zero. |
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