Matteo Focardi

ON THE VARIATIONAL APPROXIMATION OF FREE-DISCONTINUITY PROBLEMS IN THE VECTORIAL CASE

We provide a variational approximation for quasiconvex energies defined on vector valued special functions with bounded variation. We extend the Ambrosio–Tortorellis construction to the vectorial case.

ASYMPTOTIC ANALYSIS OF AMBROSIO-TORTORELLI ENERGIES IN LINEARIZED ELASTICITY ∗

We provide an approximation result in the sense of

Fracture mechanics in perforated domains: A variational model for brittle porous media

\Gamma

A 1D Macroscopic Phase Field Model for Dislocations and a Second Order

-convergence for energies of the form

\Gamma

\int_\Omega\mathscr{Q}_1(e(u))\,dx+a\,\mathcal{H}^{n-1}(J_u)+b\,\int_{J_u}\mathscr{Q}_0^{1/2}([u]\odot\nu_u)\,d\mathcal{H}^{n-1}

-Limit

, where

Which special functions of bounded deformation have bounded variation

\Omega\subset\mathbb{R}^n

On the Measure and the Structure of the Free Boundary of the Lower Dimensional Obstacle Problem

is a bounded open set with Lipschitz boundary,

Integral Representation for Functionals Defined on SBD p in Dimension Two

\mathscr{Q}_0

Homogenization of Random Fractional Obstacle Problems via Γ-Convergence

and