Given an open, bounded and connected set A ⊂ Rn with Lipschitz boundary and volume |A|, we prove that the sequence Fk of Dirichlet functionals defined on H1(A;Rd), with volume constraints v^k on m ≥ 2 fixed level-sets, and such that Sum_i v^k_i< |A| for all k, Gamma-converges, as v^k → v with Sum_i v_i = |A|, to the squared total variation on 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
2003-01-01
Abstract
Given an open, bounded and connected set A ⊂ Rn with Lipschitz boundary and volume |A|, we prove that the sequence Fk of Dirichlet functionals defined on H1(A;Rd), with volume constraints v^k on m ≥ 2 fixed level-sets, and such that Sum_i v^k_i< |A| for all k, Gamma-converges, as v^k → v with Sum_i v_i = |A|, to the squared total variation on BV(A;Rd), with v as volume constraint on the same level-sets.File in questo prodotto:
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