Stable solutions for the bilaplacian with exponential nonlinearity
| 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 | Let $λ^*>0$ denote the largest possible value of $λ$ such that \begin{align*} \left\{\begin{aligned} Δ^2 u & = \la e^u && \text{in $B $} u &= \pd{u}{n} = 0 && \text{on $ \pa B $} \end{aligned} \right. \end{align*} has a solution, where $B$ is the unit ball in $\R^N$ and $n$ is the exterior unit normal vector. We show that for $λ=λ^*$ this problem possesses a unique {\em weak} solution $u^*$. We prove that $u^*$ is smooth if $N\le 12$ and singular when $N\ge 13$, in which case $ u^*(r) = - 4 \log r + \log (8(N-2)(N-4) / λ^*) + o(1)$ as $r\to 0$. We also consider the problem with general constant Dirichlet boundary conditions. | |
| dc.identifier | https://arxiv.org/abs/0801.2445 | |
| dc.identifier | http://arxiv.org/abs/0801.2445 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146068 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Stable solutions for the bilaplacian with exponential nonlinearity | |
| dc.type | text |