The Parabolic Two-Phase Membrane Problem: Regularity in Higher Dimensions
| dc.creator | Shahgholian, Henrik | |
| dc.creator | Uraltseva, Nina | |
| dc.creator | Weiss, Georg S. | |
| dc.date | 2007-12-20 | |
| dc.date.accessioned | 2026-07-07T08:50:36Z | |
| dc.date.available | 2026-07-07T08:50:36Z | |
| dc.description | For the parabolic obstacle-problem-like equation $$Δu - \partial_t u = λ_+ χ_{\{u>0\}} - λ_- χ_{\{u<0\}} ,$$ where $λ_+$ and $λ_-$ are positive Lipschitz functions, we prove in arbitrary finite dimension that the free boundary $\partial\{u>0\} \cup\partial\{u<0\}$ is in a neighborhood of each ``branch point'' the union of two Lipschitz graphs that are continuously differentiable with respect to the space variables. The result extends the elliptic paper \cite{imrn} to the parabolic case. The result is optimal in the sense that the graphs are in general not better than Lipschitz, as shown by a counter-example. | |
| dc.identifier | https://arxiv.org/abs/0712.3411 | |
| dc.identifier | http://arxiv.org/abs/0712.3411 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144655 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35R35; 35J60 | |
| dc.title | The Parabolic Two-Phase Membrane Problem: Regularity in Higher Dimensions | |
| dc.type | text |