PDE seminar: Asymptotic behavior of least energy solutions for a 2D nonlinear Neumann problem with large exponent

2013-11-18 16:30 - 2013-11-18 17:30
Faculty of Science Building #3, Room 309
Futoshi Takahashi (Osaka City University)
In this talk, we consider a semilinear elliptic problem
with the nonlinear Neumann boundary condition in
two dimension. We discuss the asymptotic behavior of
least energy solutions to the problem when the nonlinear
exponent $p$ gets large. We show that the least
energy solutions remain bounded uniformly in $p$,
and it develops one peak on the boundary, the location
of which is controlled by the Green function associated
to the linear problem.