The Relative Capacity
| dc.creator | Biegert, Markus | |
| dc.date | 2008-06-09 | |
| dc.date | 2008-07-10 | |
| dc.date.accessioned | 2026-07-07T09:49:18Z | |
| dc.date.available | 2026-07-07T09:49:18Z | |
| dc.description | The purpose of this article is to introduce the relative $p$-capacity $\Cap_{p,Ω}$ with respect to an open set $Ω$ in $\IR^N$. It is a Choquet capacity on the closure of $Ω$ and extends the classical $p$-capacity $\Cap_p$ in the sense that $\Cap_{p,Ω}=\Cap_p$ if $Ω=\IR^N$. The importance of the relative $p$-capacity stems from the fact that a large class of Sobolev functions defined on a 'bad domain' admit a trace on the boundary $\partialΩ$ which is then unique up to $\Cap_{p,Ω}$-polar set. As an application we prove a characterization of $W^{1,p}_0(Ω)$ for open sets $Ω\subset\IR^N$. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/0806.1417 | |
| dc.identifier | http://arxiv.org/abs/0806.1417 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164533 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 31B15 | |
| dc.title | The Relative Capacity | |
| dc.type | text |