Optimal boundary regularity for some singular Monge-Ampère equations on bounded convex domains
Keyword(s):
<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ \det D^2 u = |u|^{-n-2-k} (x\cdot Du -u)^{-k} $\end{document}</tex-math></inline-formula> with zero boundary data, have unexpected degenerate nature.</p>
2018 ◽
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pp. 271-305
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2001 ◽
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pp. 235-256
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2018 ◽
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pp. 6873-6890
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pp. 429-443
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Keyword(s):
1985 ◽
Vol 26
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pp. 115-120
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