On singular strictly convex solutions to the Monge-Amp\`ere equation
Analysis of PDEs
2023-11-16 v1
Abstract
We show the existence of a strictly convex function with associated Monge-Amp\`ere measure represented by a function with a.e. whose Hessian has a singular part. This extends the work [13] and answers an open question of [14,Sec. 6.2(1)].
Cite
@article{arxiv.2311.08848,
title = {On singular strictly convex solutions to the Monge-Amp\`ere equation},
author = {Guido De Philippis and Riccardo Tione},
journal= {arXiv preprint arXiv:2311.08848},
year = {2023}
}