Strong maximum principle for generalized solutions to equations of the Monge-Ampère type

2024/03/31 by Jian, Huaiyu, Tu, Xushan · 1 citation
#35B50 #35J96 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.00609

Abstract

In this paper, we investigate the strong maximum principle for generalized solutions of Monge-Ampère type equations. We prove that the strong maximum principle holds at points where the function is strictly convex but not necessarily C^1,1 smooth, and show that it fails at non-strictly convex points. The results we obtain can be applied to various Minkowski type problems in convex geometry by the virtue of the Gauss image map.

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