Γ-convergence approach to variational problems in perforated domains with Fourier boundary conditions
Open Access
- 19 December 2008
- journal article
- Published by EDP Sciences in ESAIM: Control, Optimisation and Calculus of Variations
- Vol. 16 (1), 148-175
- https://doi.org/10.1051/cocv:2008073
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.Keywords
This publication has 13 references indexed in Scilit:
- Averaging in a perforated domain with an oscillating third boundary conditionSbornik: Mathematics, 2001
- Спектральные асимптотики для одной стационарной задачи теплопроводности в перфорированной областиMatematicheskie Zametki, 2001
- Asymptotic behavior of a solution to a boundary value problem in a perforated domain with oscillating boundarySiberian Mathematical Journal, 1998
- A Strange Term Coming from NowherePublished by Springer Science and Business Media LLC ,1997
- On the nature of the temperature distribution in a perforated body with given values on the external boundary under conditions of heat transfer by Newton's law on the boundary of the cavitiesSbornik: Mathematics, 1996
- Tartar's method of compensated compactness in averaging the spectrum of a mixed problem for an elliptic equation in a perforated domain with third boundary conditionSbornik: Mathematics, 1995
- An Introduction to Γ-ConvergencePublished by Springer Science and Business Media LLC ,1993
- An extension theorem from connected sets, and homogenization in general periodic domainsNonlinear Analysis, 1992
- Asymptotic analysis of two elliptic equations with oscillating termsESAIM: Mathematical Modelling and Numerical Analysis, 1988
- Homogenization in open sets with holesJournal of Mathematical Analysis and Applications, 1979