Mathematics – Functional Analysis
Scientific paper
2011-09-21
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
DeJarnette Noel
Hajlasz Piotr
Lukyanenko Anton
Tyson Jeremy
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