-convergence of constrained Dirichlet functionals
Gian Paolo Leonardi (2003)
Bollettino dell'Unione Matematica Italiana
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Given an open, bounded and connected set with Lipschitz boundary and volume , we prove that the sequence of Dirichlet functionals defined on , with volume constraints on fixed level-sets, and such that for all , -converges, as with , to the squared total variation on , with as volume constraint on the same level-sets.