The Lipschitz extension problem with prescribed local Lipschitz constants and eikonal mappings

Document Type

Article

Publication Date

2026

Abstract

Let Gamma be a closed subset of a complete Riemannian manifold M of dimension >= 2, let f : M -> N be a Lipschitz map to a complete Riemannian manifold N, and let psi be a continuous function which dominates the local Lipschitz constant of f. We construct a Lipschitz map which agrees with f on Gamma and whose local Lipschitz constant is psi.

Keywords

Kirszbraun-Valentine theorem, Lipschitz extension, Local Lipschitz constant, Eikonal equation

Publication Title

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

DOI

10.1016/j.jmaa.2025.129826

Volume

553

Issue

1

First Page

129826

Publisher

Academic Press

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