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Gamma-Convergence for Beginners$
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Andrea Braides

Print publication date: 2002

Print ISBN-13: 9780198507840

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198507840.001.0001

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*DIRICHLET PROBLEMS IN PERFORATED DOMAINS

*DIRICHLET PROBLEMS IN PERFORATED DOMAINS

Chapter:
(p.171) 13*DIRICHLET PROBLEMS IN PERFORATED DOMAINS
Source:
Gamma-Convergence for Beginners
Author(s):

Andrea Braides

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198507840.003.0014

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.

Keywords:   Dirichlet conditions, joining lemma, phase transition, capacitary problem, Cioranescu-Murat strange term

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