Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-24T15:54:28.378Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite-difference approximation of free-discontinuity problems

Published online by Cambridge University Press:  12 July 2007

Massimo Gobbino  and
Maria Giovanna Mora
Massimo Gobbino
Affiliation:
Università degli Studi di Pisa, Dipartimento di Matematica Applicata 'Ulisse Dini', via Bonanno 25B, 56126 Pisa, Italy ([email protected])
Maria Giovanna Mora
Affiliation:
SISSA, via Beirut 2/4, 34014 Trieste, Italy ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We approximate functionals depending on the gradient of u and on the behaviour of u near the discontinuity points by families of non-local functionals where the gradient is replaced by finite differences. We prove pointwise convergence, Γ-convergence and a compactness result, which implies, in particular, the convergence of minima and minimizers.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 3 , June 2001 , pp. 567 - 595
Copyright
Copyright © Royal Society of Edinburgh 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)