Strong maximum principle for generalized solutions to equations of the Monge-Amp\`ere type
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 C1,1 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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