Results 211 to 220 of about 409,387 (264)

Approximation of Free-Discontinuity Problems

1998
Andrea Braides
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Non-local approximation of free-discontinuity problems in linear elasticity and application to stochastic homogenisation

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2022
We analyse the $\Gamma$-convergence of general non-local convolution type functionals with varying densities depending on the space variable and on the symmetrized gradient.
R. Marziani, Francesco Solombrino
semanticscholar   +1 more source

A compactness result in $$GSBV^p$$GSBVp and applications to $$\varGamma $$Γ-convergence for free discontinuity problems

Calculus of Variations and Partial Differential Equations, 2018
We present a compactness result in the space $$GSBV^p$$GSBVp which extends the classical statement due to Ambrosio (Arch Ration Mech 111:291–322, 1990) to problems without a priori bounds on the functions.
Manuel Friedrich
semanticscholar   +1 more source

A discontinuous nonlinear eigenvalue/Free boundary problem

Mathematical Methods in the Applied Sciences, 1982
AbstractWe study the problem (H is the Heaviside unit step function) in spherical domains Ω of arbitrary dimension. When g = 0, there are two branches of radial solutions; for small nonzero g there are solutions near the corresponding radial solution. Moreover, the set where μ = 1 is in all cases an analytic hypersurface.
Roger Alexander, P. H. Rabinowitz
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FREE DISCONTINUITY PROBLEMS WITH UNBOUNDED DATA

Mathematical Models and Methods in Applied Sciences, 1994
We prove the existence of a minimizing pair for a free discontinuity problem, i.e. a variational problem in which the unknowns are a closed set K and a function suitably smooth outside K. Examples of such problems come from pattern recognition and mathematical physics, when both “volume” energy and “surface” energy are present.
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Minimisers of Free Discontinuity Problems

2000
Abstract In this chapter and in the next one we study existence and regularity of solutions of a class of free discontinuity problems whose model is the Mumford-Shah functional introduced in Chapter 4.
Luigi Ambrosio, Nicola Fusco, Diego Pallara   +2 more
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Variational Problems with a Free Discontinuity Set

1994
The present chapter is a short survey about the most recent contributions to the mathematical analysis of a variational approach to image segmentation proposed by D. Mumford and J. Shah.
LEACI, Antonio, S. SOLIMINI
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Discrete approximation of a free discontinuity problem

Numerical Functional Analysis and Optimization, 1994
We approximate by discrete Г-convergence a functional proposed by Mumford-Shah for a variational approach to image segmentation. Such a functional is first relaxed with a sequence of nonconvex functionals, which in turn, are dis-cretized by piecewise linear finite elements. Under a suitable relation between the relaxation parameter ∊and the meshsize h,
BELLETTINI, GIOVANNI, Coscia, A.
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Functions of Bounded Variation and Free Discontinuity Problems

2000
Abstract 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 problems'. The aim of this book is twofold: The first three chapters present all the basic prerequisites for the treatment of free discontinuity ...
AMBROSIO, Luigi, FUSCO N., PALLARA D.
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On the approximation of free discontinuity problems

1992
This paper compliments another one of the authors [Commun. Pure Appl. Math. 43, No. 8, 999-1036 (1990; Zbl 0722.49020)] both concerning the approximation (in the sense of \(\Gamma\)-convergence) of the Mumford-Shah type functional (or rather its lower semicontinuous envelope) by elliptic functionals which formally have simpler form.
AMBROSIO L, TORTORELLI, VINCENZO MARIA
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