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Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains

TitleConcentration at curves for a singularly perturbed Neumann problem in three-dimensional domains
Publication TypeJournal Article
Year of Publication2005
AuthorsMalchiodi, A
JournalGeometric and Functional Analysis 15 (6) 1162-1222 (2005)
Abstract

We prove new concentration phenomena for the equation −ɛ2 Δu + u = up in a smooth bounded domain R3 and with Neumann boundary conditions. Here p > 1 and ɛ > 0 is small. We show that concentration of solutions occurs at some geodesics of ∂Ω when ɛ → 0.

URLhttp://hdl.handle.net/1963/4866
DOI10.1007/s00039-005-0542-7

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