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 dynamical problems linked to such functionals many approximations by functionals defined on smooth functions have been proposed (using high-order singular perturbations, finite-difference or non-local energies, etc.) The purpose of this book is to present a global approach to these approximations using the theory of gamma-convergence and of special functions of bounded variation. The book is directed to PhD students and researchers in calculus of variations, interested in approximation problems with possible applications.

Keywords

Approximation
Volume
calculus of variations s
computer vision
fracture mechanics
functional analysis
partial differential equations

Bibliographic Information

Book Title: Approximation of Free-Discontinuity Problems
Authors: Andrea Braides
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0097344
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1998
Softcover ISBN: 978-3-540-64771-3Published: 17 September 1998
eBook ISBN: 978-3-540-68714-6Published: 13 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIV, 154
Topics: Partial Differential Equations, Numerical Analysis, Theoretical, Mathematical and Computational Physics

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Table of contents (6 chapters)

Front Matter

Introduction

Functions of bounded variation

Special functions of bounded variation

Examples of approximation

A general approach to approximation

Non-local approximation

Back Matter

About this book

Keywords

Bibliographic Information

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