Une méthode de construction des bornes supérieures pour des problèmes de perturbation singulières

Translated title of the contribution: A method for establishing upper bounds for singular perturbation problems

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Abstract

We present two applications of a new method for proving upper bounds for singular perturbation problems involving maps of bounded variation. The two problems are of first and second order, respectively. The first is a minimization problem, related to the question of optimal lifting for BV-maps with values in S1, for which we prove a Γ-convergence result. The second problem involves the Aviles-Giga functional, ε ∫Ω2v 2dx + 1/ε ∫Ω (1 - ∇v 2)2 dx, for which we construct upper bounds via a sequence of functions whose limit has gradient in BV.

Translated title of the contributionA method for establishing upper bounds for singular perturbation problems
Original languageFrench
Pages (from-to)97-102
Number of pages6
JournalComptes Rendus Mathematique
Volume341
Issue number2
DOIs
StatePublished - 15 Jul 2005
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics

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