Explicit solutions of Jensen's auxiliary equations via extremal Lipschitz extensions

2019/07/22 by Fernando Charro, Charro, Fernando
Mathematics · #35J70 #46T20 #49K20 #54E40 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Equations Stability Results #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1907.09214

openalex publication_date 2019/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we prove that McShane and Whitney's Lipschitz extensions are viscosity solutions of Jensen's auxiliary equations, known to have a key role in Jensen's celebrated proof of uniqueness of infinity harmonic functions, and therefore of Absolutely Minimizing Lipschitz Extensions. To the best of the author's knowledge, this result does not appear to be known in the literature in spite of the vast amount of work around the topic.

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