Regularity for the Monge–Ampère equation by doubling

Ravi Shankar; Yu Yuan

doi:10.1007/s00209-024-03508-6

Regularity for the Monge–Ampère equation by doubling

Ravi Shankar
, Yu Yuan

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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 language	English (US)
Article number	34
Journal	Mathematische Zeitschrift
Volume	307
Issue number	2
DOIs	https://doi.org/10.1007/s00209-024-03508-6
State	Published - Jun 2024

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00209-024-03508-6

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title = "Regularity for the Monge–Amp{\`e}re equation by doubling",

abstract = "We give a new proof for the interior regularity of strictly convex solutions of the Monge–Amp{\`e}re 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.",

author = "Ravi Shankar and Yu Yuan",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.",

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AB - 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.

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Regularity for the Monge–Ampère equation by doubling

Abstract

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