Given an open, bounded and connected set A ⊂ Rn with Lipschitz boundary and volume |A|, we prove that the sequence Fk of Dirich-let functionals defined on H1(A;Rd), with volume constraints vk onm ≥ 2 fixed level-sets, and such thatPmi=1vki< || for all k, Gamma-converges, as vk → v withPmi=1vi = |A|, to the squared total variationon BV (A;Rd), with v as volume constraint on the same level-sets.
Gamma-convergence of constrained Dirichlet functionals / Leonardi, Gian Paolo. - In: BOLLETTINO DELL'UNIONE MATEMATICA ITALIANA. B. - ISSN 0392-4041. - STAMPA. - 6B:2(2003), pp. 339-351.
Gamma-convergence of constrained Dirichlet functionals
LEONARDI, Gian Paolo
2003
Abstract
Given an open, bounded and connected set A ⊂ Rn with Lipschitz boundary and volume |A|, we prove that the sequence Fk of Dirich-let functionals defined on H1(A;Rd), with volume constraints vk onm ≥ 2 fixed level-sets, and such thatPmi=1vki< || for all k, Gamma-converges, as vk → v withPmi=1vi = |A|, to the squared total variationon BV (A;Rd), with v as volume constraint on the same level-sets.
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