TY - JOUR
T1 - Concentration of least-energy solutions to a semilinear Neumann problem in thin domains
AU - Maeda, Masaya
AU - Suzuki, Kanako
PY - 2014/3/15
Y1 - 2014/3/15
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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U2 - 10.1016/j.jmaa.2013.09.036
DO - 10.1016/j.jmaa.2013.09.036
M3 - Article
AN - SCOPUS:84887824771
SN - 0022-247X
VL - 411
SP - 465
EP - 484
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -