arXiv:2404.00609 Abstract | arXiv Analytics

arXiv:2404.00609 [math.AP]Abstract References Reviews Resources

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

Published 2024-03-31Version 1

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.

Comments: Strong maximum principle, Monge-Amp\`ere equation, Strict convexity, Uniqueness

Categories: math.AP

Subjects: 35B50, 35J96

Keywords: generalized solutions, monge-ampère type, strong maximum principle holds, minkowski type problems, gauss image map

Related articles: Most relevant | Search more

arXiv:1912.12896 [math.AP] (Published 2019-12-30)

Generalized solutions to models of compressible viscous fluids

Anna Abbatiello, Eduard Feireisl, Antonin Novotny

arXiv:0906.4233 [math.AP] (Published 2009-06-23)

Self-similar blow-up in parabolic equations of Monge--Ampère type

C. R. Budd, V. A. Galaktionov

arXiv:1805.09085 [math.AP] (Published 2018-05-23)