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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])
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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

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