Irene Fonseca

Relaxation of multiple integrals below the growth exponent

Abstract The integral representation of the relaxed energies F q,p (u,Ω):= inf {u n } lim inf n→∞ ∫ Ω F(ϰ u n ,▽u n )dϰ :u n ∈ W 1,q (Ω,R d ), u n ≮ u weakly in W 1,p (Ω,R d ) , F loc q,p (u,Ω):= inf {u n } lim inf n→∞ ∫ Ω F(ϰ u n ,▽u n )dϰ :u n ∈ W loc 1,q (Ω,R d ), u n ≮ u weakly in W 1,p (Ω,R d ) of a functional E: u ∈ ∞ Ω F(ϰ, u, ▽ u)dϰ, u ∈: W 1,q (Ω,R d ) , where 0 ≥ F (ϰ,ζ,ξ) ≥ (1+|ζ|r + |ξ|q and max 1,r N−1 N + r ,q −1 N , is studied. In particular, W1,p-sequential weak lower semicontinuity of E(·) is obtained in the case where F = F(ξ) is a quasiconvex function and p > q(N − 1)/N.

Second order singular perturbation models for phase transitions

Singular perturbation models involving a penalization of the first order derivatives have provided a new insight into the role played by surface energies in the study of phase transitions problems. It is known that if

A HIGHER ORDER MODEL FOR IMAGE RESTORATION: THE ONE-DIMENSIONAL CASE ∗

W:{\mathbb R}^d \to [0,+\infty)

Dynamics for Systems of Screw Dislocations

grows at least linearly at infinity and it has exactly two potential wells of level zero at

Relaxation of convex functionals : the gap problem

a, b \in {\mathbb R}^d

Higher-Order Quasiconvexity Reduces to Quasiconvexity

, then the

On the total variation of the Jacobian

\Gamma(L^1)

Regularity in Time for Weak Solutions of a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surfaces

-limit of the family of functionals

NONLOCAL CHARACTER OF THE REDUCED THEORY OF THIN FILMS WITH HIGHER ORDER PERTURBATIONS

{\mathcal F}_\varepsilon(u):= \begin{cases} \int_{\Omega} \left(\frac{W(u)}{\varepsilon}+\varepsilon \vert \nabla u\vert^2\right) \, dx & \hbox{ if