Sur un problème de minimisation lié au relévement des fonctions BV à valeurs dans S1

Arkady Poliakovsky

doi:10.1016/j.crma.2004.09.030

Sur un problème de minimisation lié au relévement des fonctions BV à valeurs dans S¹

Translated title of the contribution: On a minimization problem related to lifting of BV functions with values in S¹

Arkady Poliakovsky

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

For u ∈ W^1,1 (Ω, S¹) denote by K the set of minimizers of the problem min ∫_Ω u ∧ ∇ u - D φ , over φ ∈ BV (Ω) satisfying ∫_Ω φ = 0. We show that an extreme point of K must be a lifting of u, up to an additive constant. We also prove a more general result for the case of u in BV (Ω, S¹).

Translated title of the contribution	On a minimization problem related to lifting of BV functions with values in S¹
Original language	French
Pages (from-to)	855-860
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	339
Issue number	12
DOIs	https://doi.org/10.1016/j.crma.2004.09.030
State	Published - 15 Dec 2004
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1016/j.crma.2004.09.030

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abstract = "For u ∈ W1,1 (Ω, S1) denote by K the set of minimizers of the problem min ∫Ω u ∧ ∇ u - D φ , over φ ∈ BV (Ω) satisfying ∫Ω φ = 0. We show that an extreme point of K must be a lifting of u, up to an additive constant. We also prove a more general result for the case of u in BV (Ω, S1).",

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N2 - For u ∈ W1,1 (Ω, S1) denote by K the set of minimizers of the problem min ∫Ω u ∧ ∇ u - D φ , over φ ∈ BV (Ω) satisfying ∫Ω φ = 0. We show that an extreme point of K must be a lifting of u, up to an additive constant. We also prove a more general result for the case of u in BV (Ω, S1).

AB - For u ∈ W1,1 (Ω, S1) denote by K the set of minimizers of the problem min ∫Ω u ∧ ∇ u - D φ , over φ ∈ BV (Ω) satisfying ∫Ω φ = 0. We show that an extreme point of K must be a lifting of u, up to an additive constant. We also prove a more general result for the case of u in BV (Ω, S1).

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DO - 10.1016/j.crma.2004.09.030

M3 - מאמר

AN - SCOPUS:10644275026

SN - 1631-073X

VL - 339

SP - 855

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 12

ER -

Sur un problème de minimisation lié au relévement des fonctions BV à valeurs dans S¹

Abstract

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