A Free boundary problem for the $p(x)$- Laplacian
| dc.creator | Bonder, Julián Fernández | |
| dc.creator | Martínez, Sandra | |
| dc.creator | Wolanski, Noemi | |
| dc.date | 2009-02-18 | |
| dc.date.accessioned | 2026-07-07T12:43:36Z | |
| dc.date.available | 2026-07-07T12:43:36Z | |
| dc.description | We consider the optimization problem of minimizing $\int_Ω|\nabla u|^{p(x)}+ λχ_{\{u>0\}} dx$ in the class of functions $W^{1,p(\cdot)}(Ω)$ with $u-ϕ_0\in W_0^{1,p(\cdot)}(Ω)$, for a given $ϕ_0\geq 0$ and bounded. $W^{1,p(\cdot)}(Ω)$ is the class of weakly differentiable functions with $\int_Ω|\nabla u|^{p(x)} dx<\infty$. We prove that every solution $u$ is locally Lipschitz continuous, that it is a solution to a free boundary problem and that the free boundary, $Ω\cap\partial\{u>0\}$, is a regular surface. | |
| dc.description | 35 pages, submitted | |
| dc.identifier | https://arxiv.org/abs/0902.3216 | |
| dc.identifier | http://arxiv.org/abs/0902.3216 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/220475 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35R35; 35B65 | |
| dc.title | A Free boundary problem for the $p(x)$- Laplacian | |
| dc.type | text |