On interior  $C^2$ -estimates for the Monge-Ampère equation

Diego Maldonado

doi:10.3934/dcds.2018058

Article Contents

2018, Volume 38, Issue 3: 1427-1440. Doi: 10.3934/dcds.2018058

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On interior $C^2$ -estimates for the Monge-Ampère equation

Diego Maldonado

Department of Mathematics, Kansas State University, 138 Cardwell Hall, Manhattan, KS 66506-0903, USA

Received: May 2017

Revised: October 2017

Published: July 2018

The author is supported by NSF grant DMS 1361754.

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Abstract

An approach towards apriori interior $C^2$-estimates for the Monge-Ampère equation based on a mean-value inequality for nonnegative subsolutions to the linearized Monge-Ampère equation is implemented.

Keywords:

Monge-Ampère equation,
linearized Monge-Ampère equation.

Mathematics Subject Classification: Primary: 35J96, 35B45; Secondary: 35B65, 35J70.

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References

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