On a singular perturbation problem related to optimal lifting in BV-space

Arkady Poliakovsky

doi:10.1007/s00526-006-0041-1

On a singular perturbation problem related to optimal lifting in BV-space

Arkady Poliakovsky

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

4 Scopus citations

Abstract

We prove a Γ-convergence result for the family of functionals defined on H ¹(Ω,;) by J_ε(φ)=∫Ω, ;(ε|∇φ|²+1/ε|u(x)-e^iφ|2p)dx, ∀ε > 0, for a given u ∈ BV(Ω,S¹) and a parameter p ∈ [1,∞) . We show that in either of the two cases, p = 2 or u ∈ W 1,1(Ω,;,S¹, any limit of the minimizers is an optimal lifting.

Original language	English
Pages (from-to)	411-426
Number of pages	16
Journal	Calculus of Variations and Partial Differential Equations
Volume	28
Issue number	4
DOIs	https://doi.org/10.1007/s00526-006-0041-1
State	Published - 1 Apr 2007
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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abstract = "We prove a Γ-convergence result for the family of functionals defined on H 1(Ω,;) by Jε(φ)=∫Ω, ;(ε|∇φ|2+1/ε|u(x)-eiφ|2p)dx, ∀ε > 0, for a given u ∈ BV(Ω,S1) and a parameter p ∈ [1,∞) . We show that in either of the two cases, p = 2 or u ∈ W 1,1(Ω,;,S1, any limit of the minimizers is an optimal lifting.",

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N2 - We prove a Γ-convergence result for the family of functionals defined on H 1(Ω,;) by Jε(φ)=∫Ω, ;(ε|∇φ|2+1/ε|u(x)-eiφ|2p)dx, ∀ε > 0, for a given u ∈ BV(Ω,S1) and a parameter p ∈ [1,∞) . We show that in either of the two cases, p = 2 or u ∈ W 1,1(Ω,;,S1, any limit of the minimizers is an optimal lifting.

AB - We prove a Γ-convergence result for the family of functionals defined on H 1(Ω,;) by Jε(φ)=∫Ω, ;(ε|∇φ|2+1/ε|u(x)-eiφ|2p)dx, ∀ε > 0, for a given u ∈ BV(Ω,S1) and a parameter p ∈ [1,∞) . We show that in either of the two cases, p = 2 or u ∈ W 1,1(Ω,;,S1, any limit of the minimizers is an optimal lifting.

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ER -

On a singular perturbation problem related to optimal lifting in BV-space

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