Calculus of Variations and Geometric Measure Theory

G. De Philippis - R. Tione

On singular strictly convex solutions to the Monge-Ampere equation

created by dephilipp on 16 Nov 2023



Inserted: 16 nov 2023
Last Updated: 16 nov 2023

Year: 2023

ArXiv: 2311.08848 PDF
Links: PDF


We show the existence of a strictly convex function $u: B_1 \to \mathbb R$ with associated Monge-Ampere measure represented by a function $f$ with $0 < f < 1$ a.e. whose Hessian has a singular part.