PHASE TRANSITIONS WITH THE LINE TENSION EFFECT: THE SUPER-QUADRATIC CASE
Giampiero Palatucci · Mathematical Models and Methods in Applied Sciences · 2009
Let Ω be an open bounded set of ℝ3 and let W and V be two non-negative continuous functions vanishing at α, β and α', β', respectively. We analyze the asymptotic behavior as ε → 0, in terms of Γ-convergence, of the following functional: [Formula: see text] where u is a scalar density function and Tu denotes its trace on ∂Ω. We show that the singular limit of the energies Fε leads to a coupled problem of bulk and surface phase transitions.