Combining solutions of semilinear partial differential equations in R^n with critical exponent
| dc.creator | Leung, Man Chun | |
| dc.date | 2002-02-23 | |
| dc.date.accessioned | 2026-07-07T04:46:39Z | |
| dc.date.available | 2026-07-07T04:46:39Z | |
| dc.description | Let $u_1$ and $u_2$ be two different positive smooth solutions of the equation $Δu + n (n - 2) u^{{n + 2}\over {n - 2}} = 0$ in $R^n (n \ge 3).$ By a result of Gidas, Ni and Nirenberg, $u_1$ and $u_2$ are radially symmetric above the points $ξ_1$ and $ξ_2$, respectively. Let $u$ be a positive $C^2$-function on $R^n$ such that $u = u_1$ in $Ω_1$ and $u = u_2$ in $Ω_2$, where $Ω_1$ and $Ω_2$ are disjoint non-empty open domains in ${\R}^n$. $u$ satisfies the equation $Δu + n (n - 2) K u^{{n + 2}\over {n - 2}} = 0$ in $R^n.$ By the same result of Gidas, Ni and Nirenberg, $K \not\equiv 1$ in $R^n$. In this paper we discuss lower bounds on $\displaystyle{\sup_{\R^n} |K - 1|} .$ Relation with decay estimates at the isolated singularity via the Kelvin transform is also considered. | |
| dc.description | 35 pages | |
| dc.identifier | https://arxiv.org/abs/math/0202243 | |
| dc.identifier | http://arxiv.org/abs/math/0202243 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63416 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Differential Geometry | |
| dc.subject | 35J60; 53C21 | |
| dc.title | Combining solutions of semilinear partial differential equations in R^n with critical exponent | |
| dc.type | text |