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 ∫Ω ∇2v 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 contribution | A method for establishing upper bounds for singular perturbation problems |
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Original language | French |
Pages (from-to) | 97-102 |
Number of pages | 6 |
Journal | Comptes Rendus Mathematique |
Volume | 341 |
Issue number | 2 |
DOIs | |
State | Published - 15 Jul 2005 |
Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics