This book deals with a class of mathematical problems which involve the minimization of the
sum of a volume and a surface energy and have lately been refered to as' free discontinuity …

Functionals involving both volume and surface energies have a number of applications
ranging from Computer Vision to Fracture Mechanics. In order to tackle numerical and …

The fascinating field of shape optimization problems has received a lot of attention in recent
years, particularly in relation to a number of applications in physics and engineering that …

This book contains both a synthesis and mathematical analysis of a wide set of algorithms
and theories whose aim is the automatic segmen tation of digital images as well as the …

The aim of this paper is to present a mathematical theory where problems of the type (0.1) inf
{ff (x, u, Vu) dx+ p (Xu u 1u) dXn.(x)} u: nc R'Rk can be stated and have a solution. In (0.1) …

Publisher Summary This chapter discusses the main properties of Γ-convergence, in
particular those that are useful in the actual computation of Γ-limits. For some classes of …

In this paper we consider a non-local anisotropic model for phase separation in two-phase
fluids at equilibrium, and show that when the thickness of the interface tends to zero in a …

An integral representation formula for a class of functionals defined on and in (the space of
special functions of bounded variation) is obtained without requiring the regularity conditions …

HOMOGENIZATION OF FREE DISCONTINUITY PROBLEMS Andrea Braides, Anneliese
Defranceschi and Enrico Vitali Introduction Following Gr Page 1 HOMOGENIZATION OF FREE …

In this survey paper we present a class of shape optimization problems where the cost
function involves the solution of a PDE of elliptic type in the unknown domain. In particular …