Differentiability of the argmin function and a minimum principle for semiconcave subsolutions

2018/08/13 by Ross, Julius, Nyström, David Witt · 1 citation
#31C99 #32U05 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.04402

Abstract

Suppose f(x,y) + \fracκ2 ‖x‖² - \fracσ2‖y‖² is convex where σ>0, and the argmin function γ(x) = \ γ: inf_y f(x,y) = f(x,γ)\ exists and is single valued. We will prove γ is differentiable almost everywhere. As an application we deduce a minimum principle for certain semiconcave subsolutions.

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