On A Class of Degenerate And Singular Monge-Amp\`ere Equations

Huaiyu Jian; You Li; Xushan Tu

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arXiv · 1908.06396

On A Class of Degenerate And Singular Monge-Amp\`ere Equations

Huaiyu Jian·You Li·Xushan Tu

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Abstract

In this paper we shall prove the existence, uniqueness and global H$\ddot{o}$lder continuity for the Dirichlet problem of a class of Monge-Amp\`ere type equations which may be degenerate and singular on the boundary of convex domains. We will establish a relation of the H$\ddot{o}$lder exponent for the solutions with the convexity for the domains.

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Huaiyu Jian, You Li, Xushan Tu. 2019-08-18. On A Class of Degenerate And Singular Monge-Amp\`ere Equations. https://arxiv.org/abs/1908.06396

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