On the relation between minimizers of a Γ-limit energy and optimal lifting in BV-space

Radu Ignat; Arkady Poliakovsky

doi:10.1142/S0219199707002496

On the relation between minimizers of a Γ-limit energy and optimal lifting in BV-space

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Abstract

We study the minimizers of an energy functional which is obtained as the Γ-limit of a family of functional depending on a small parameter ε > 0, associated with a function u ∈ BV(Ω, S¹) and a positive parameter p. We find necessary and sufficient conditions on p and the dimension under which these minimizers coincide with the optimal liftings of u, for every u ∈ BV(Ω, S¹).

Original language	English
Pages (from-to)	447-472
Number of pages	26
Journal	Communications in Contemporary Mathematics
Volume	9
Issue number	4
DOIs	https://doi.org/10.1142/S0219199707002496
State	Published - 1 Aug 2007
Externally published	Yes

Keywords

Functions of bounded variation
Lifting
Γ-limit

ASJC Scopus subject areas

Mathematics (all)
Applied Mathematics

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10.1142/S0219199707002496

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N2 - We study the minimizers of an energy functional which is obtained as the Γ-limit of a family of functional depending on a small parameter ε > 0, associated with a function u ∈ BV(Ω, S1) and a positive parameter p. We find necessary and sufficient conditions on p and the dimension under which these minimizers coincide with the optimal liftings of u, for every u ∈ BV(Ω, S1).

AB - We study the minimizers of an energy functional which is obtained as the Γ-limit of a family of functional depending on a small parameter ε > 0, associated with a function u ∈ BV(Ω, S1) and a positive parameter p. We find necessary and sufficient conditions on p and the dimension under which these minimizers coincide with the optimal liftings of u, for every u ∈ BV(Ω, S1).

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On the relation between minimizers of a Γ-limit energy and optimal lifting in BV-space

Abstract

Keywords

ASJC Scopus subject areas

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