Finite-difference approximation of free-discontinuity problems
Published online by Cambridge University Press: 12 July 2007
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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