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Research Article | Open Access

A monotonicity approach to Pogorelov's Hessian estimates for Monge- Ampère equation

Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195, USA
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Abstract

We present an integral approach to Pogorelov's Hessian estimates for the Monge-Ampère equation, originally obtained via a pointwise argument.

Keywords

Monge-Ampère equation

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Mathematics in Engineering
Volume 5 Issue 2,
April 2023
Pages 1-6
DOI: 10.3934/mine.2023037

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Cite this article:
Yuan Y. A monotonicity approach to Pogorelov's Hessian estimates for Monge- Ampère equation. Mathematics in Engineering, 2023, 5(2): 1-6. https://doi.org/10.3934/mine.2023037

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Received: 21 April 2022
Revised: 25 May 2022
Accepted: 25 May 2022
Published: 15 April 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)