Perturbing singular solutions of the Gelfand problem
| dc.creator | Davila, Juan | |
| dc.creator | Dupaigne, Louis | |
| dc.creator | Guerra, Ignacio | |
| dc.creator | Montenegro, Marcelo | |
| dc.date | 2008-01-16 | |
| dc.date.accessioned | 2026-07-07T08:54:48Z | |
| dc.date.available | 2026-07-07T08:54:48Z | |
| dc.description | he equation $-Δu = λe^u$ posed in the unit ball $B \subseteq \R^N$, with homogeneous Dirichlet condition $u|_{\partial B} = 0$, has the singular solution $U=\log\frac1{|x|^2}$ when $λ= 2(N-2)$. If $N\ge 4$ we show that under small deformations of the ball there is a singular solution $(u,λ)$ close to $(U,2(N-2))$. In dimension $N\ge 11$ it corresponds to the extremal solution -- the one associated to the largest $λ$ for which existence holds. In contrast, we prove that if the deformation is sufficiently large then even when $N\ge 10$, the extremal solution remains bounded in many cases. | |
| dc.identifier | https://arxiv.org/abs/0801.2441 | |
| dc.identifier | http://arxiv.org/abs/0801.2441 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146067 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Perturbing singular solutions of the Gelfand problem | |
| dc.type | text |