The precise boundary trace of positive solutions of the equation $Δu=u^q$ in the supercritical case
| dc.creator | Marcus, Moshe | |
| dc.creator | Veron, Laurent | |
| dc.date | 2006-10-03 | |
| dc.date.accessioned | 2026-07-07T07:28:38Z | |
| dc.date.available | 2026-07-07T07:28:38Z | |
| dc.description | We construct the precise boundary trace of positive solutions of $Δu=u^q$ in a smooth bounded domain in $R^N$, for $q$ in the super-critical range $q\geq (N+1)/(N-1)$. The construction is performed in the framework of the fine topology associated with the Bessel capacity $C_{2/q,q'}$ on the boundary of the domain. We prove that the boundary trace is a Borel measure (in general unbounded), which is outer regular relative to this capacity. We provide a necessary and sufficient condition for such measures to be the boundary trace of a positive solution and prove that the corresponding generalized boundary value problem is well-posed in the class of $σ$-moderate solutions. | |
| dc.description | 39 pages | |
| dc.identifier | https://arxiv.org/abs/math/0610102 | |
| dc.identifier | http://arxiv.org/abs/math/0610102 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117802 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Primary 35J60, 35J67; Secondary 31B15, 31B20, 31C15 | |
| dc.title | The precise boundary trace of positive solutions of the equation $Δu=u^q$ in the supercritical case | |
| dc.type | text |