Growth estimates on positive solutions of the equation $Δu + K u^{{n + 2}\over {n - 2}} = 0$ in ${\R}^n$
| dc.creator | Leung, Man Chun | |
| dc.date | 2000-02-01 | |
| dc.date.accessioned | 2026-07-07T04:33:32Z | |
| dc.date.available | 2026-07-07T04:33:32Z | |
| dc.description | We construct unbounded positive $C^2$-solutions of the equation $Δu + K u^{(n + 2)/(n - 2)} = 0$ in ${\R}^n$ (equipped with Euclidean metric $g_o$) such that $K$ is bounded between two positive numbers in ${\R}^n$, the conformal metric $g = u^{4/(n - 2)} g_o$ is complete, and the volume growth of $g$ can be arbitrarily fast or reasonably slow according to the constructions. By imposing natural conditions on $u$, we obtain growth estimate on the $L^{2n/(n - 2)}$-norm of the solution and show that it has slow decay. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0002005 | |
| dc.identifier | http://arxiv.org/abs/math/0002005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58608 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Differential Geometry | |
| dc.subject | 35J60; 53C21 | |
| dc.title | Growth estimates on positive solutions of the equation $Δu + K u^{{n + 2}\over {n - 2}} = 0$ in ${\R}^n$ | |
| dc.type | text |