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Title: Optimal boundary regularity for some singular Monge-Ampère equations on bounded convex domains

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 \begin{document}$ \det D^2 u = |u|^{-n-2-k} (x\cdot Du -u)^{-k} $\end{document} with zero boundary data, have unexpected degenerate nature.

 
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Award ID(s):
2054686
NSF-PAR ID:
10327289
Author(s) / Creator(s):
Date Published:
Journal Name:
Discrete & Continuous Dynamical Systems
Volume:
42
Issue:
5
ISSN:
1078-0947
Page Range / eLocation ID:
2199
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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