Calculus of Variations and Geometric Measure Theory

F. Cagnetti - L. Scardia

An extension theorem in $SBV$ and an application to the homogenization of the Mumford-Shah functional in perforated domains

created by scardia on 06 Oct 2008
modified by cagnetti on 13 Nov 2013


Published Paper

Inserted: 6 oct 2008
Last Updated: 13 nov 2013

Journal: J. Math. Pures Appl.
Volume: 95
Pages: 349-381
Year: 2011


The aim of this paper is to prove the existence of extension operators for $SBV$ functions from periodically perforated domains. This result will be the fundamental tool to prove the compactness in a non coercive homogenization problem.

Keywords: Homogenization, Brittle fracture, $\Gamma$-convergence, extension theorem