Nam Q. Le

collaborators

3 papers

math.AP2025

Large dimension behavior of the Hessian eigenvalues of the unit balls

Nam Q. Le

We show that a sequence of $k$ -Hessian eigenvalues of the unit ball in $R^{n}$ stays bounded as long as the ratio $n / k$ 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 equatio…

math.AP2024

Global $C^{1, β}$ and $W^{2, p}$ regularity for some singular Monge-Ampère equations

Nam Q. Le, Ovidiu Savin

We establish global $C^{1, β}$ and $W^{2, p}$ regularity for singular Monge-Ampère equations of the form \[\det D^2 u \sim \text{dist}^{-α}(\cdot,\partialΩ),\quad α\in (0, 1),\] und…

Large dimension behavior of the Hessian eigenvalues of the unit balls

Global Lipschitz and Sobolev estimates for the Monge-Ampère eigenfunctions of general bounded convex domains

Global C1,β and W2,p regularity for some singular Monge-Ampère equations

Global $C^{1, β}$ and $W^{2, p}$ regularity for some singular Monge-Ampère equations