Γ-Convergence of some super quadratic functionals with singular weights

摘要

We study the Γ-convergence of the following functional (p > 2) where Ω is an open bounded set of ? and W and V are two non-negative continuous functions vanishing at α, β and α′, β′, respectively. In the previous functional, we fix a = 2 - p and u is a scalar density function, Tu denotes its trace on ?Ω, d(x, ?Ω) stands for the distance function to the boundary ?Ω. We show that the singular limit of the energies Fε leads to a coupled problem of bulk and surface phase transitions.