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Approximation of Free-Discontinuity Problems

  • Book
  • © 1998

Overview

Authors:
  1. Andrea Braides
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1694)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-XI
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  2. Introduction

    • Andrea Braides
    Pages 1-6

  3. Functions of bounded variation

    • Andrea Braides
    Pages 7-26

  4. Special functions of bounded variation

    • Andrea Braides
    Pages 27-38

  5. Examples of approximation

    • Andrea Braides
    Pages 39-86

  6. A general approach to approximation

    • Andrea Braides
    Pages 87-102

  7. Non-local approximation

    • Andrea Braides
    Pages 103-130

  8. Back Matter

    Pages 131-150
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Keywords

About this book

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.

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