Generalized hyperbolic harmonic functions in the plane
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review
Details
| Original language | English |
|---|---|
| Title of host publication | Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014) |
| Publisher | American Institute of Physics Inc. |
| Volume | 1648 |
| ISBN (Print) | 9780735412873 |
| DOIs | |
| Publication status | Published - 10 Mar 2015 |
| Publication type | A4 Article in a conference publication |
| Event | International Conference of Numerical Analysis and Applied Mathematics - , Greece Duration: 1 Jan 2000 → … |
Conference
| Conference | International Conference of Numerical Analysis and Applied Mathematics |
|---|---|
| Country | Greece |
| Period | 1/01/00 → … |
Abstract
We consider solutions of the equation yΔh (x,y)-k ah/ay=0 in the plane. These functions already have been investigated by Weinstein around 1950 in connection of generalized axially symmetric potential theory. We have found several results concerning these type of functions, called k-hyperbolic harmonic functions, in higher dimensions. In this paper, we show in the plane case that it is possible to compute the explicit fundamental solutions in terms of the hyperbolic metric. These results may be used to find fundamental solutions in all even dimensional spaces. The key tools are the transformation properties of hyperbolic metric of the Poincaré upper half space model.
ASJC Scopus subject areas
Keywords
- axially symmetric, fundamental solution, Hyperbolic, Laplace-Beltrami