Calculus of Variations and Geometric Measure Theory

G. P. Leonardi

Gamma-convergence of constrained Dirichlet functionals

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


Published Paper

Inserted: 18 sep 2001
Last Updated: 17 dec 2006

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


Given $\Omega$ subset of $*R*^n$, which is open, connected and bounded, with Lipschitz boundary and volume $
$, 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 $
$ for all $k$, gamma-converges, as $*v*^k$ tends to $*v*$ with $v_1+...+v_m =
$, to the squared total variation on $BV(\Omega;*R*^d)$, with $*v*$ as volume constraint on the same level-sets.