English

Regularity for the Monge-Amp\`ere equation by doubling

Analysis of PDEs 2023-11-30 v1 Differential Geometry

Abstract

We give a new proof for the interior regularity of strictly convex solutions of the Monge-Amp\`ere equation. Our approach uses a doubling inequality for the Hessian in terms of the extrinsic distance function on the maximal Lagrangian submanifold determined by the potential equation.

Keywords

Cite

@article{arxiv.2311.17291,
  title  = {Regularity for the Monge-Amp\`ere equation by doubling},
  author = {Ravi Shankar and Yu Yuan},
  journal= {arXiv preprint arXiv:2311.17291},
  year   = {2023}
}

Comments

7 pages

R2 v1 2026-06-28T13:34:52.586Z