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Approximation of free-discontinuity problems by elliptic functionals via -convergence

Summary: Approximation of free-discontinuity problems
by elliptic functionals via -convergence
Emilio Acerbi
Dipartmento dif Matematica, Universit`a di Parma
via D'Azeglio 85a, Parma
Andrea Braides
SISSA, via Beirut 4, 34014 Trieste, Italy
1 Introduction
A variational formulation of some problems in Computer Vision was given by
Mumford and Shah [14], and later elaborated by De Giorgi and Ambrosio [11]. In
this framework, problems involving the functional

dx + Hn-1
(Su), (1)
defined on the space SBV () of special functions of bounded variation are stud-
ied, where u denotes the approximate gradient of u, and Su is the set of the
discontinuity points of u. In a two-dimensional setting, Su represents the contours
of the object in a picture and u is a smoothing of an imput image. Energies of the
same form arise in fracture mechanics for brittle solids, where Su is interpreted


Source: Acerbi, Emilio - Dipartimento di Matematica, UniversitÓ degli Studi di Parma


Collections: Mathematics