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 language | English |
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Pages (from-to) | 465-484 |
Number of pages | 20 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 411 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2014 Mar 15 |
Keywords
- Least-energy solutions
- Semilinear elliptic equation
ASJC Scopus subject areas
- Analysis
- Applied Mathematics