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Non-local approximation of free-discontinuity problemswith linear growth

Published online by Cambridge University Press:  14 February 2007

Luca Lussardi  and
Enrico Vitali
Luca Lussardi
Affiliation:
Dipartimento di Matematica “F. Casorati” Via Ferrata 1, 27100, Pavia, Italy;  luca.lussardi@unipv.it
Enrico Vitali
Affiliation:
Dipartimento di Matematica “F. Casorati” Via Ferrata 1, 27100, Pavia, Italy;  luca.lussardi@unipv.it
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Abstract

We approximate, in the sense ofΓ-convergence, free-discontinuity functionals with lineargrowth in the gradient by a sequence of non-local integralfunctionals depending on the average of the gradients on smallballs. The result extends to higher dimension what we already proved inthe one-dimensional case.

Keywords

Variational approximationfree discontinuities.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 1 , January 2007 , pp. 135 - 162
Copyright
© EDP Sciences, SMAI, 2007

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