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.
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}
}
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7 pages