On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target

Details On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target

2011-09-21

arxiv.org/abs/1109.4641v1

Mathematics

Functional Analysis

Scientific paper

We study the question: When are Lipschitz mappings dense in the Sobolev space $W^{1,p}(M,H^n)$? Here $M$ denotes a compact Riemannian manifold with or without boundary, while $H^n$ denotes the $n$th Heisenberg group equipped with a sub-Riemannian metric. We show that Lipschitz maps are dense in $W^{1,p}(M,H^n)$ for all $1\le p<\infty$ if $\dim M \le n$, but that Lipschitz maps are not dense in $W^{1,p}(M,H^n)$ if $\dim M \ge n+1$ and $n\le p

Affiliated with

Also associated with

No associations

Rating

On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target 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 the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-261355