3 papers
math.AP2026
Global and regularity for some singular Monge-Ampère equations
Nam Q. Le, Ovidiu Savin
We establish global and regularity for singular Monge-Ampère equations of the form \[\det D^2 u \sim \text{dist}^{-α}(\cdot,\partialΩ),\quad α\in (0, 1),\…
math.AP2025
Large dimension behavior of the Hessian eigenvalues of the unit balls
Nam Q. Le
We show that a sequence of -Hessian eigenvalues of the unit ball in stays bounded as long as the ratio stays bounded. Moreover, we identify their growth of…
math.AP2025
Global Lipschitz and Sobolev estimates for the Monge-Ampère eigenfunctions of general bounded convex domains
Nam Q. Le
We show that the Monge-Ampère eigenfunctions of general bounded convex domains are globally Lipschitz. The same result holds for convex solutions to degenerate Monge-Ampère equat…