English

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 u:B1Ru: B_1 \to \mathbb{R} with associated Monge-Amp\`ere measure represented by a function ff with 0<f<10 < f < 1 a.e. whose Hessian has a singular part. This extends the work [13] and answers an open question of [14,Sec. 6.2(1)].

Keywords

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}
}