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Optimal boundary regularity for some singular Monge-Ampère equations on bounded convex domains
Nam Q. Le
By constructing explicit supersolutions, we obtain the optimal global Hölder regularity for several singular Monge-Ampère equations on general bounded open convex domains including…
A spectral characterization and an approximation scheme for the Hessian eigenvalue
Nam Q. Le
We revisit the -Hessian eigenvalue problem on a smooth, bounded, -convex domain in . First, we obtain a spectral characterization of the -Hessian eigenval…
Solvability of a class of singular fourth order equations of Monge-Ampère type
Nam Q. Le, Bin Zhou
We study the solvability of the second boundary value problem for a class of highly singular fourth order equations of Monge-Ampère type. They arise in the approximation of convex…
Uniqueness for a system of Monge-Ampère equations
Nam Q. Le
In this note, we prove a uniqueness result, up to a positive multiplicative constant, for nontrivial convex solutions to a system of Monge-Ampère equations \begin{equation*} \left\…
Global estimates for the Monge-Ampère equation on polygonal domains in the plane
Nam Q. Le, Ovidiu Savin
We classify global solutions of the Monge-Ampère equation on the first quadrant in the plane with quadratic boundary data. As an application, we obtain global $C^{2…
On approximating minimizers of convex functionals with a convexity constraint by singular Abreu equations without uniform convexity
Nam Q. Le
We revisit the problem of approximating minimizers of certain convex functionals subject to a convexity constraint by solutions of fourth order equations of Abreu type. This approx…