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We prove that under some structure and decay hypotheses, limits of discrete systems with multi-neighbourhood interactions give rise to local energies with bulk and surface part.

These Lecture Notes cover the course given at SISSA by AB in Spring 2000 (Chapters 1 and 2) and some general results just hinted at in the course (Chapter 3). They include mainly results by the authors and by Chambolle, Dal Maso, Garroni and Truskinovsky, but some results are new; e.g., Sections 1.4{1.8 (except 1.4.1 and 1.7.2), and Section 3.3.

This paper deals with fracture mechanics in periodically perforated domains. Our aim is to provide a variational model for brittle porous media. For the sake of simplicity we will restrict our analysis to the case of anti-planar elasticity. Given the perforated domain Ωε ⊂ R N (ε being an internal scale representing the size of the periodically distributed… (More)

In recent years the stability of the isoperimetric and related inequalities has been the object of many investigations. Roughly speaking, given the well known isoperimetric property of balls, the question is how far a set E ⊂ R is from the unit ball B1 if |E| = |B1| and its perimeter P (E) is close to the perimeter of B1. The first results in this direction… (More)

We study the asymptotic limit of obstacle problems for Mumford-Shah type functionals with p-growth in periodically-perforated domains via the Γ-convergence of the associated freediscontinuity energies. In the limit a non-trivial penalization term related to the 1-capacity of the reference hole appears if and only if the size of the perforation scales like ε… (More)

In recent works L.C. Evans has noticed a strong analogy between Mather’s theory of minimal measures in Lagrangian dynamic and the theory developed in the last years for the optimal mass transportation (or MongeKantorovich) problem. In this paper we start to investigate this analogy by proving that to each minimal measure it is possible to associate, in a… (More)

- Roberto Alicandro, Maria Stella Gelli
- SIAM J. Math. Analysis
- 2016

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