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

Masaya Maeda; Kanako Suzuki

doi:10.1016/j.jmaa.2013.09.036

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

Masaya Maeda, Kanako Suzuki

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We consider the following semilinear elliptic equation: Here, ε>0 and p>1 Ω_ε is a domain in R2 with smooth boundary ∂Ω_ε, and ν denotes the outer unit normal to ∂Ω_ε. The domain Ω_ε 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 language	English
Pages (from-to)	465-484
Number of pages	20
Journal	Journal of Mathematical Analysis and Applications
Volume	411
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2013.09.036
Publication status	Published - 2014 Mar 15

Keywords

Least-energy solutions
Semilinear elliptic equation

ASJC Scopus subject areas

Analysis
Applied Mathematics

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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.",

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AU - Suzuki, Kanako

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N2 - 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.

AB - 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.

KW - Least-energy solutions

KW - Semilinear elliptic equation

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