Calculus of Variations and Geometric Measure Theory

N. De Ponti - J. Somaglia

Global Lipschitz extension preserving the slope

created by deponti on 28 Jul 2025

[BibTeX]

Preprint

Inserted: 28 jul 2025
Last Updated: 28 jul 2025

Year: 2025

Abstract:

We show that every real-valued Lipschitz function on a subset of a metric space can be extended to the whole space while preserving the slope and, up to a small error, the global Lipschitz constant. This answers a question posed by Di Marino, Gigli, and Pratelli, who established the analogous property for the asymptotic Lipschitz constant. We also prove the same result for the ascending slope and for the descending slope.


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