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arXiv · 2404.00609

Strong maximum principle for generalized solutions to equations of the Monge-Amp\`ere type

Huaiyu Jian·Xushan Tu
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Abstract

In this paper, we investigate the strong maximum principle for generalized solutions of Monge-Amp\`ere 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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Huaiyu Jian, Xushan Tu. 2024-03-31. Strong maximum principle for generalized solutions to equations of the Monge-Amp\`ere type. https://arxiv.org/abs/2404.00609

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