*DIRICHLET PROBLEMS IN PERFORATED DOMAINS
This chapter discusses a direct treatment of problems in perforated domains with a Dirichlet condition on the perforation. It relies on a joining lemma by Ansini and Braides, allowing the decoupling of the problem close and far away from the perforation, based on the well-known procedure of De Giorgi to treat boundary conditions. The contribution close to the perforation gives a higher-dimensional version of a phase-transition energy that can be expressed through a capacitary problem, recovering the ‘strange term’ of the Cioranescu-Murat approach to the same problem.
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