The Relative Capacity

Details The Relative Capacity The Relative Capacity

2008-06-09

arxiv.org/abs/0806.1417v3

Mathematics

Analysis of PDEs

20 pages

Scientific paper

The purpose of this article is to introduce the relative $p$-capacity $\Cap_{p,\Omega}$ with respect to an open set $\Omega$ in $\IR^N$. It is a Choquet capacity on the closure of $\Omega$ and extends the classical $p$-capacity $\Cap_p$ in the sense that $\Cap_{p,\Omega}=\Cap_p$ if $\Omega=\IR^N$. 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 $\partial\Omega$ which is then unique up to $\Cap_{p,\Omega}$-polar set. As an application we prove a characterization of $W^{1,p}_0(\Omega)$ for open sets $\Omega\subset\IR^N$.

Affiliated with

Also associated with

No associations

Rating

The Relative Capacity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Relative Capacity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Relative Capacity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-400641