Local minimisers and singular perturbations

Robert Kohn, Peter Sternberg

Research output: Contribution to journalArticle

Abstract

We construct local minimisers to certain variational problems. The method is quite general and relies on the theory of F-convergence. The approach is demonstrated through the model problem [formula ommittes] It is shown that in certain nonconvex domains The approach is demonstrated through the model problem Ω ⊂Rn and for ε small, there exist nonconstant localminimisers uε satisfying uε≃±1 except in a thin transition layer. The location of the layer is determined through the requirement that in the limit uε→u() the hypersurface separating the states u0= 1 and u0=-1 locally minimises surface area. Generalisations are discussed with, for example, vector-valued u and anisotropic perturbations replacing’∇u2.

Original languageEnglish (US)
Pages (from-to)69-84
Number of pages16
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume111
Issue number1-2
DOIs
StatePublished - 1989

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Singular Perturbation
Transition Layer
Thin Layer
Surface area
Variational Problem
Hypersurface
Perturbation
Minimise
Requirements
Model
Generalization

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Local minimisers and singular perturbations. / Kohn, Robert; Sternberg, Peter.

In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol. 111, No. 1-2, 1989, p. 69-84.

Research output: Contribution to journalArticle

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