A minimum problem with free boundary in Orlicz spaces
| dc.creator | Martinez, Sandra | |
| dc.creator | Wolanski, Noemi | |
| dc.date | 2006-02-17 | |
| dc.date | 2007-08-02 | |
| dc.date.accessioned | 2026-07-07T08:21:47Z | |
| dc.date.available | 2026-07-07T08:21:47Z | |
| dc.description | We consider the optimization problem of minimizing $\int_ΩG(|\nabla u|)+λχ_{\{u>0\}} dx$ in the class of functions $W^{1,G}(Ω)$ with $u-ϕ_0\in W_0^{1,G}(Ω)$, for a given $ϕ_0\geq 0$ and bounded. $W^{1,G}(Ω)$ is the class of weakly differentiable functions with $\int_ΩG(|\nabla u|) dx<\infty$. The conditions on the function G allow for a different behavior at 0 and at $\infty$. We prove that every solution u is locally Lipschitz continuous, that they are solution to a free boundary problem and that the free boundary, $\partial\{u>0\}\cap Ω$, is a regular surface. Also, we introduce the notion of weak solution to the free boundary problem solved by the minimizers and prove the Lipschitz regularity of the weak solutions and the $C^{1,α}$ regularity of their free boundaries near ``flat'' free boundary points. | |
| dc.identifier | https://arxiv.org/abs/math/0602388 | |
| dc.identifier | http://arxiv.org/abs/math/0602388 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135435 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J20, 35P30, 49K20 | |
| dc.title | A minimum problem with free boundary in Orlicz spaces | |
| dc.type | text |