Rigidity results for some boundary quasilinear phase transitions
| dc.creator | Sire, Yannick | |
| dc.creator | Valdinoci, Enrico | |
| dc.date | 2008-03-10 | |
| dc.date.accessioned | 2026-07-07T09:25:56Z | |
| dc.date.available | 2026-07-07T09:25:56Z | |
| dc.description | We consider a quasilinear equation given in the half-space, i.e. a so called boundary reaction problem. Our concerns are a geometric Poincaré inequality and, as a byproduct of this inequality, a result on the symmetry of low-dimensional bounded stable solutions, under some suitable assumptions on the nonlinearities. More precisely, we analyze the following boundary problem $$ \left\{\begin{matrix} -{\rm div} (a(x,|\nabla u|)\nabla u)+g(x,u)=0 \qquad {on $\R^n\times(0,+\infty)$} -a(x,|\nabla u|)u_x = f(u) \qquad{\mbox{on $\R^n\times\{0\}$}}\end{matrix} \right.$$ under some natural assumptions on the diffusion coefficient $a(x,|\nabla u|)$ and the nonlinearities $f$ and $g$. Here, $u=u(y,x)$, with $y\in\R^n$ and $x\in(0,+\infty)$. This type of PDE can be seen as a nonlocal problem on the boundary $\partial \R^{n+1}_+$. The assumptions on $a(x,|\nabla u|)$ allow to treat in a unified way the $p-$laplacian and the minimal surface operators. | |
| dc.identifier | https://arxiv.org/abs/0803.1382 | |
| dc.identifier | http://arxiv.org/abs/0803.1382 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156578 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J70, 35J65, 47G30, 35B45 | |
| dc.title | Rigidity results for some boundary quasilinear phase transitions | |
| dc.type | text |