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Γ-convergence approach to variational problemsin perforated domains with Fourier boundary conditions

Published online by Cambridge University Press:  19 December 2008

Valeria Chiadò Piat  and
Andrey Piatnitski
Valeria Chiadò Piat
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy.
Andrey Piatnitski
Affiliation:
Narvik University College, HiN, Postbox 385, 8505, Narvik, Norway and Lebedev Physical Institute RAS, Leninski prospect 53, Moscow 119991, Russia. andrey@sci.lebedev.ru
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Abstract

The work focuses on the Γ-convergence problem and the convergence of minimizers for a functional defined in a periodic perforated medium andcombining the bulk (volume distributed) energy and the surfaceenergy distributed on the perforation boundary. It is assumed that the mean valueof surface energy at each level set of test function is equal tozero.Under natural coercivity and p-growth assumptions on the bulk energy, and the assumption that the surface energy satisfies p-growth upper bound, weshow that the studied functional has a nontrivial Γ-limit andthe corresponding variational problem admitshomogenization.


Keywords

HomogenizationΓ-convergenceperforated medium
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 1 , January 2010 , pp. 148 - 175
Copyright
© EDP Sciences, SMAI, 2008

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