Maximal solutions of equation u = uq in arbitrary domains
| dc.creator | Marcus, Moshe | |
| dc.creator | Veron, Laurent | |
| dc.date | 2008-05-24 | |
| dc.date.accessioned | 2026-07-07T12:19:12Z | |
| dc.date.available | 2026-07-07T12:19:12Z | |
| dc.description | We prove bilateral capacitary estimates for the maximal solution $U_F$ of $-Δu+u^q=0$ in the complement of an arbitrary closed set $F\subset\mathbb R^N$, involving the Bessel capacity $C_{2,q'}$, for $q$ in the supercritical range $q\geq q_{c}:=N/(N-2)$. We derive a pointwise necessary and sufficient condition, via a Wiener type criterion, in order that $U_F(x)\to\infty$ as $x\to y$ for given $y\in\prt F$. Finally we prove a general uniqueness result for large solutions. | |
| dc.identifier | https://arxiv.org/abs/0805.3787 | |
| dc.identifier | http://arxiv.org/abs/0805.3787 | |
| dc.identifier | Comptes Rendus de l Académie des Sciences - Series I - Mathematics 344 (2007) 299-304 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212674 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J60 | |
| dc.title | Maximal solutions of equation u = uq in arbitrary domains | |
| dc.type | text |