Concentration of least-energy solutions to a semilinear Neumann problem in thin domains

Masaya Maeda, Kanako Suzuki

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We consider the following semilinear elliptic equation: Here, ε>0 and p>1 Ωε is a domain in R2 with smooth boundary ∂Ωε, and ν denotes the outer unit normal to ∂Ωε. The domain Ωε depends on ε, which shrinks to a straight line in the plane as ε→0. In this case, a least-energy solution exists for each ε sufficiently small, and it concentrates on a line. Moreover, the concentration line converges to the narrowest place of the domain as ε→0.

Original languageEnglish
Pages (from-to)465-484
Number of pages20
JournalJournal of Mathematical Analysis and Applications
Volume411
Issue number2
DOIs
Publication statusPublished - 2014 Mar 15

Keywords

  • Least-energy solutions
  • Semilinear elliptic equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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