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arXiv · 2610.35192

Global regularity for a class of degenerate/singular Monge-Ampere equations

Fan Cui·Huaiyu Jian·You Li·Yannan Liu
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Abstract

We study the global regularity of solutions to the homogeneous Dirichlet problem for a class of Monge-Ampere equations, which become degenerate or singular on the boundary due to the zero boundary value and the distance function. The degeneracy and singularity are described by the index - the sum of the powers of the distance function and the solution. We give a complete classification of the index, and prove that the solution is globally Holder continuous, log-Lipschitz continuous, $C^{1,eta}$, $C^{2,alpha}$ and $W^{2,p}$ respectively, depending on the size of the index. We also obtain estimates related to the five regularity results. All these results are optimal.

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Fan Cui, Huaiyu Jian, You Li, Yannan Liu. 2026-10-26. Global regularity for a class of degenerate/singular Monge-Ampere equations. https://arxiv.org/abs/2610.35192

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