On a Capacity for Modular Spaces

Details On a Capacity for Modular Spaces On a Capacity for Modular Spaces

2009-01-08

arxiv.org/abs/0901.1036v1

Mathematics

Functional Analysis

Scientific paper

The purpose of this article is to define a capacity on certain topological measure spaces $X$ with respect to certain function spaces $V$ consisting of measurable functions. In this general theory we will not fix the space $V$ but we emphasize that $V$ can be the classical Sobolev space $W^{1,p}(\Omega)$, the classical Orlicz-Sobolev space $W^{1,\Phi}(\Omega)$, the Haj{\l}asz-Sobolev space $M^{1,p}(\Omega)$, the Musielak-Orlicz-Sobolev space (or generalized Orlicz-Sobolev space) and many other spaces. Of particular interest is the space $V:=\tW^{1,p}(\Omega)$ given as the closure of $W^{1,p}(\Omega)\cap C_c(\overline\Omega)$ in $W^{1,p}(\Omega)$. In this case every function $u\in V$ (a priori defined only on $\Omega$) has a trace on the boundary $\partial\Omega$ which is unique up to a $\Cap_{p,\Omega}$-polar set.

Affiliated with

Also associated with

No associations

Rating

On a Capacity for Modular Spaces 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 On a Capacity for Modular Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On a Capacity for Modular Spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-62624