Regularity for the Monge–Ampère equation by doubling

Ravi Shankar, Yu Yuan

Research output: Contribution to journalArticlepeer-review

Abstract

We give a new proof for the interior regularity of strictly convex solutions of the Monge–Ampère 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.

Original languageEnglish (US)
Article number34
JournalMathematische Zeitschrift
Volume307
Issue number2
DOIs
StatePublished - Jun 2024

All Science Journal Classification (ASJC) codes

  • General Mathematics

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