Local minimisers and singular perturbations

Robert V. Kohn, Peter Sternberg

Research output: Contribution to journalArticlepeer-review


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
Issue number1-2
StatePublished - 1989

ASJC Scopus subject areas

  • General Mathematics


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