Global Lipschitz and Sobolev estimates for the Monge–Ampère eigenfunctions of general bounded convex domains
Abstract
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 equations of the form det D 2 u = M | u | p with zero boundary condition on general bounded convex domains in ℝ n within the sharp threshold p > n - 2 . As a consequence, we obtain global W 2 , 1 estimates for these solutions.
Fields of Study & Subjects
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Annales de la faculté des sciences de Toulouse Mathématiques
- Volume
- 35
- Issue
- 2
- Pages
- 467–487
- Publication date
- 12 June 2026
- Language
- EN