Ana Cristina Barroso

Anisotropic Singular Perturbations The Vectorial Case

We obtain the Γ( L 1 (Ώ))-limit of the sequence where E e is the family of anisotropic perturbations of the nonconvex functional of vector-valued functions The proof relies on the blow-up argument introduced by Fonseca and Muller.

Relaxation of bulk and interfacial energies

AbstractIn this paper we obtain an integral representation for the relaxation inBV(Ω; ℝp) of the functional

Coupled second order singular perturbations for phase transitions

u \mapsto \int\limits_\Omega {f(x.\nabla u(x))dx + \int\limits_{\sum _{(u)} } {\varphi (x,[u](x),v(x))dH_{N - 1} (x)} }

Differential inclusions for differential forms

with respect to theBV weak * convergence.

Necessary and sufficient conditions for existence of solutions of a variational problem involving the curl

Second-order structured deformations of continua provide an extension of the multiscale geometry of first-order structured deformations by taking into account the effects of submacroscopic bending and curving. We derive here an integral representation for a relaxed energy functional in the setting of second-order structured deformations. Our derivation covers inhomogeneous initial energy densities (i.e., with explicit dependence on the position); finally, we provide explicit formulas for bulk relaxed energies as well as anticipated applications.

EXPLICIT FORMULAS FOR RELAXED DISARRANGEMENT DENSITIES ARISING FROM STRUCTURED DEFORMATIONS

The asymptotic behaviour of a family of singular perturbations of a non-convex second order functional of the type is studied through Γ-convergence techniques as a variational model to address two-phase transition problems.