Special Session 70: Progress and Challenges in Nonlocal and Nonhomogeneous PDEs

Periodically perforated energies in the nonlocal setting
Giampiero Palatucci
University of Parma
Italy
Co-Author(s):    Matteo Focardi; Caterina Ida Zeppieri
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.