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2007
Issue 64

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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., $π_{1} (Y) = π_{2} (Y) = \dots = π_{[p]} (Y) = 0$ , where $[p]$ is the largest integer less than or equal to $p$ .

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Received:: 06.07.07

Published:: 06.07.07

MSC Codes:: 46E35

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