Differentiability of the Argmin Function and a Minimum Principle for Semiconcave Subsolutions

Journal article, 2020

Suppose f(x, y) + k/2 parallel to x parallel to(2 )- sigma/2 parallel to y parallel to(2) is convex where kappa >= 0 sigma > 0, and the argmin function gamma(x) = {gamma : inf(y) f(x, y) = f(x, gamma)} exists and is single valued. We will prove gamma is differentiable almost everywhere. As an application we deduce a minimum principle for certain semiconcave subsolutions.