# American Institute of Mathematical Sciences

doi: 10.3934/dcds.2021188
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## Optimal boundary regularity for some singular Monge-Ampère equations on bounded convex domains

 Department of Mathematics, Indiana University, Bloomington, 831 E 3rd St, Bloomington, IN 47405, USA

*Corresponding author: Nam Q. Le

Received  April 2021 Early access December 2021

Fund Project: The author is supported by NSF grant DMS-2054686

By constructing explicit supersolutions, we obtain the optimal global Hölder regularity for several singular Monge-Ampère equations on general bounded open convex domains including those related to complete affine hyperbolic spheres, and proper affine hyperspheres. Our analysis reveals that certain singular-looking equations, such as $\det D^2 u = |u|^{-n-2-k} (x\cdot Du -u)^{-k}$ with zero boundary data, have unexpected degenerate nature.

Citation: Nam Q. Le. Optimal boundary regularity for some singular Monge-Ampère equations on bounded convex domains. Discrete & Continuous Dynamical Systems, doi: 10.3934/dcds.2021188
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