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

Abstract

In this note we prove that McShane and Whitney's Lipschitz extensions are viscosity solutions of Jensen's auxiliary equations which are 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 on the topic.