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.

Finite-difference approximation of free-discontinuity problems

GOBBINO, MASSIMO;
2001-01-01

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.
2001
Gobbino, Massimo; Mora, M. G.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/178724
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