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MiS Preprint
64/2007
Density of Lipschitz mappings in the class of Sobolev mappings between metric spaces
Piotr Hajlasz
Abstract
We prove that Lipschitz mappings are dense in the Newtonian-Sobolev class $N^{1,p}(X,Y)$ of mappings from spaces $X$ supporting $p$-Poincar\'e inequalities into a finite Lipschitz polyhedron $Y$ if and only if $Y$ is $[p]$-connected i.e., $\pi_1(Y)=\pi_2(Y)=\ldots=\pi_{[p]}(Y)=0$, where $[p]$ is the largest integer less than or equal to $p$.
