The Two-Phase Membrane Problem -- an Intersection-Comparison Approach to the Regularity at Branch Points
| dc.creator | Shahgholian, Henrik | |
| dc.creator | Weiss, Georg S. | |
| dc.date | 2005-02-01 | |
| dc.date.accessioned | 2026-07-07T05:16:34Z | |
| dc.date.available | 2026-07-07T05:16:34Z | |
| dc.description | For the two-phase membrane problem $ Δu = {λ_+\over 2} χ_{\{u>0\}} - {λ_-\over 2} χ_{\{u<0\}} ,$ where $λ_+> 0$ and $λ_->0 ,$ we prove in two dimensions that the free boundary is in a neighborhood of each ``branch point'' the union of two $C^1$-graphs. We also obtain a stability result with respect to perturbations of the boundary data. Our analysis uses an intersection-comparison approach based on the Aleksandrov reflection. In higher dimensions we show that the free boundary has finite $(n-1)$-dimensional Hausdorff measure. | |
| dc.identifier | https://arxiv.org/abs/math/0502015 | |
| dc.identifier | http://arxiv.org/abs/math/0502015 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74036 | |
| dc.subject | Analysis of PDEs | |
| dc.title | The Two-Phase Membrane Problem -- an Intersection-Comparison Approach to the Regularity at Branch Points | |
| dc.type | text |