# Gamma-convergence of constrained Dirichlet functionals

created on 18 Sep 2001
modified by leonardi on 17 Dec 2006

[BibTeX]

Published Paper

Inserted: 18 sep 2001
Last Updated: 17 dec 2006

Journal: Boll. UMI
Volume: 6-B
Number: 8
Pages: 339-351
Year: 2003

Abstract:

Given $\Omega$ subset of $*R*^n$, which is open, connected and bounded, with Lipschitz boundary and volume $\Omega$, we prove that a sequence $F_k$ of Dirichlet-type functionals defined on $H^1(\Omega;*R*^d)$, with volume constraints $*v*^k$ on $m$ fixed level-sets, and such that the sum of $v^k_i$ over $i=1..m$ is less than $\Omega$ for all $k$, gamma-converges, as $*v*^k$ tends to $*v*$ with $v_1+...+v_m = \Omega$, to the squared total variation on $BV(\Omega;*R*^d)$, with $*v*$ as volume constraint on the same level-sets.

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