Stationary isothermic surfaces and some characterizations of the hyperplane in the N-dimensional Euclidean space
| dc.creator | Magnanini, Rolando | |
| dc.creator | Sakaguchi, Shigeru | |
| dc.date | 2008-12-11 | |
| dc.date.accessioned | 2026-07-07T12:12:02Z | |
| dc.date.available | 2026-07-07T12:12:02Z | |
| dc.description | We consider an entire graph S of a continuous real function over (N-1)-dimensional Euclidean space with N larger than or equal to 3. Let D be a domain in N-dimensional Euclidean space with S as a boundary. Consider in D the heat flow with initial temperature 0 and boundary temperature 1. The problem we consider is to characterize S in such a way that there exists a stationary isothermic surface in D. We show that S must be a hyperplane under some general conditions on S. This is related to Liouville or Bernstein-type theorems for some elliptic Monge-Ampère-type equation. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/0812.2165 | |
| dc.identifier | http://arxiv.org/abs/0812.2165 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210413 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35K05; 35K20; 35J60; 35J25 | |
| dc.title | Stationary isothermic surfaces and some characterizations of the hyperplane in the N-dimensional Euclidean space | |
| dc.type | text |