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Density of Lipschitz mappings in the class of Sobolev mappings between metric spaces

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Abstract

We prove that Lipschitz mappings are dense in the Newtonian–Sobolev classes N 1,p(X, Y) of mappings from spaces X supporting p-Poincaré inequalities into a finite Lipschitz polyhedron Y if and only if Y is [p]-connected, π 1(Y) = π 2(Y) = · · · = π [p](Y) = 0, where [p] is the largest integer less than or equal to p.

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  1. Department of Mathematics, University of Pittsburgh, 301 Trackeray Hall, Pittsburgh, PA, 15260, USA

    Piotr Hajłasz

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  1. Piotr Hajłasz
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Correspondence to Piotr Hajłasz.

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This work was supported by the NSF grant DMS-0500966.

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Hajłasz, P. Density of Lipschitz mappings in the class of Sobolev mappings between metric spaces. Math. Ann. 343, 801–823 (2009). https://doi.org/10.1007/s00208-008-0291-7

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