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

¹ Dipartimento di Matematica, Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy.
² Narvik University College, HiN, Postbox 385, 8505, Narvik, Norway and Lebedev Physical Institute RAS, Leninski prospect 53, Moscow 119991, Russia. andrey@sci.lebedev.ru

Received: 3 November 2007
Revised: 24 June 2008

Abstract

The work focuses on the Γ-convergence problem and the convergence of minimizers for a functional defined in a periodic perforated medium and combining the bulk (volume distributed) energy and the surface energy distributed on the perforation boundary. It is assumed that the mean value of surface energy at each level set of test function is equal to zero. Under natural coercivity and p-growth assumptions on the bulk energy, and the assumption that the surface energy satisfies p-growth upper bound, we show that the studied functional has a nontrivial Γ-limit and the corresponding variational problem admits homogenization.