Explicit solutions of Jensen's auxiliary equations via extremal Lipschitz extensions
Texas State University, Department of Mathematics
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.
Lipschitz extension, McShane-Whitney extension, Infinity Laplacian
Charro, F. (2020). Explicit solutions of Jensen's auxiliary equations via extremal Lipschitz extensions. <i>Electronic Journal of Differential Equations, 2020</i>(37), pp. 1-6.
Attribution 4.0 International