Henon type equations and concentration on spheres
Ederson Moreira dos SantosF. Pacella
35B0635B0735B4035J1535J61Henon-type problemsConcentration phenomenaSymmetry
In this paper, we study the concentration profile of various kinds of symmetric solutions of some semilinear elliptic problems arising in astrophysics and in diffusion phenomena. Using a reduction method, we prove that doubly symmetric positive solutions in a $2m$-dimensional ball must concentrate and blow up on $(m-1)$-spheres as the concentration parameter tends to infinity. We also consider axially symmetric positive solutions in a ball in $\mathbb{R}^N$, $N\geq3$, and show that concentration and blow-up occur on two antipodal points, as the concentration parameter tends to infinity.
Indiana University Mathematics Journal
2016
text
pdf
10.1512/iumj.2016.65.5751
10.1512/iumj.2016.65.5751
en
Indiana Univ. Math. J. 65 (2016) 273 - 306
state-of-the-art mathematics
http://iumj.org/access/