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Γ-limits of convolutionfunctionals

Published online by Cambridge University Press:  23 January 2013

Luca Lussardi  and
Annibale Magni
Luca Lussardi
Affiliation:
Dipartimento di Matematica e Fisica “N. Tartaglia”, Università Cattolica del Sacro Cuore, via dei Musei 41, 25121 Brescia, Italy. l.lussardi@dmf.unicatt.it
Annibale Magni
Affiliation:
Mathematisches Institut Abt. für Reine Mathematik, Albert-Ludwigs Universität Freiburg, Eckerstrasse 1, 79104 Freiburg im Breisgau, Germany; annibale.magni@math.uni-freiburg.de
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Abstract

We compute the Γ-limit of a sequence of non-local integral functionalsdepending on a regularization of the gradient term by means of a convolution kernel. Inparticular, as Γ-limit, we obtain free discontinuity functionals withlinear growth and with anisotropic surface energy density.

Keywords

Free discontinuitiesΓ-convergenceanisotropy
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 2 , April 2013 , pp. 486 - 515
Copyright
© EDP Sciences, SMAI, 2013

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