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

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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.

Original languageEnglish
Pages (from-to)411-426
Number of pages16
JournalCalculus of Variations and Partial Differential Equations
Volume28
Issue number4
DOIs
StatePublished - 1 Apr 2007
Externally publishedYes

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