We study the limit behaviour of singularly-perturbed elliptic functionals of the form F k (u,
v)=∫ A v 2 fk (x,∇ u) dx+ 1 ε k∫ A gk (x, v, ε k∇ v) dx, where u is a vector-valued Sobolev …

A variational model proposed in the physics literature to describe the onset of pattern
formation in two-component bilayer membranes and amphiphilic monolayers leads to the …

In this paper, we study the asymptotics of singularly perturbed phase-transition functionals of
the formℱ k (u)= 1/ε k∫ A fk (𝑥, u, ε k∇ u) d𝑥, where u∈[0, 1] is a phase-field variable, ε k> …

the function u= bχE+ aχΩ\E is a solution of problem (P0). Here LN stands for the N-
dimensional Lebesgue measure. This lack of uniqueness is due the fact that interfaces …

We propose and study two variants of the Ambrosio--Tortorelli functional where the first-
order penalization of the edge variable v is replaced by a second-order term depending on …

We derive a macroscopic limit for a sharp interface version of a model proposed in Komura
et al.(Langmuir 22: 6771–6774, 2006) to investigate pattern formation due to competition of …

In this paper we studythe asymptotics of singularly perturbed phase-transition functionals of
the form\[F_k (u)=\frac {1}{\epsilon_k}\int_A f_k (x, u,\epsilon_k\nabla u)\, dx\,,\] where $ u\in …

We consider mass-constrained minimizers for a class of non-convex energy functionals
involving a double-well potential. Based upon global quadratic lower bounds to the energy …

We study the effective behavior of random, heterogeneous, anisotropic, second-order phase
transitions energies that arise in the study of pattern formations in physical–chemical …

In this thesis, we derive a macroscopic limit for a sharp interface version of a modelproposed
by Komura, Shimokawa and Andelman (2006) to investigate pattern formationdue to …