Blow-up solutions of nonlinear elliptic 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 | For an integer $n \ge 3$ and any positive number $ε$ we establish the existence of smooth functions K on $R^n \setminus \{0 \}$ with $|K - 1| \le ε$, such that the equation $Δu + n (n - 2) K u^{{n + 2}\over {n - 2}} = 0$ in $R^n \setminus \{0 \}$ has a smooth positive solution which blows up at the origin (i.e., u does not have slow decay near the origin). Furthermore, we show that in some cases K can be extended as a Lipschitz function on ${\R}^n.$ These provide counter-examples to a conjecture of C.-S. Lin when n > 4, and Taliaferro's conjecture. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/math/0202244 | |
| dc.identifier | http://arxiv.org/abs/math/0202244 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63417 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Differential Geometry | |
| dc.subject | 35J60; 53C21 | |
| dc.title | Blow-up solutions of nonlinear elliptic equations in R^n with critical exponent | |
| dc.type | text |