Continuity estimates for the Monge - Ampère equation

Huai Yu Jian; Xu Jia Wang

doi:10.1137/060669036

Continuity estimates for the Monge - Ampère equation

Huai Yu Jian^*, Xu Jia Wang

^*Corresponding author for this work

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

37 Citations (Scopus)

Abstract

In this paper, we study the regularity of solutions to the Monge-Ampère equation. We prove the log-Lipschitz continuity for the gradient under certain assumptions. We also give a unified treatment for the continuity estimates of the second derivatives. As an application we show the local existence of continuous solutions to the semigeostrophic equation arising in meteorology.

Original language	English
Pages (from-to)	608-626
Number of pages	19
Journal	SIAM Journal on Mathematical Analysis
Volume	39
Issue number	2
DOIs	https://doi.org/10.1137/060669036
Publication status	Published - 2007

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title = "Continuity estimates for the Monge - Amp{\`e}re equation",

abstract = "In this paper, we study the regularity of solutions to the Monge-Amp{\`e}re equation. We prove the log-Lipschitz continuity for the gradient under certain assumptions. We also give a unified treatment for the continuity estimates of the second derivatives. As an application we show the local existence of continuous solutions to the semigeostrophic equation arising in meteorology.",

keywords = "A priori estimates, Monge - Amp{\`e}re equation, Semigeostrophic equation",

author = "Jian, {Huai Yu} and Wang, {Xu Jia}",

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T1 - Continuity estimates for the Monge - Ampère equation

AU - Jian, Huai Yu

AU - Wang, Xu Jia

PY - 2007

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N2 - In this paper, we study the regularity of solutions to the Monge-Ampère equation. We prove the log-Lipschitz continuity for the gradient under certain assumptions. We also give a unified treatment for the continuity estimates of the second derivatives. As an application we show the local existence of continuous solutions to the semigeostrophic equation arising in meteorology.

AB - In this paper, we study the regularity of solutions to the Monge-Ampère equation. We prove the log-Lipschitz continuity for the gradient under certain assumptions. We also give a unified treatment for the continuity estimates of the second derivatives. As an application we show the local existence of continuous solutions to the semigeostrophic equation arising in meteorology.

KW - A priori estimates

KW - Monge - Ampère equation

KW - Semigeostrophic equation

UR - http://www.scopus.com/inward/record.url?scp=41449092797&partnerID=8YFLogxK

U2 - 10.1137/060669036

DO - 10.1137/060669036

M3 - Article

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VL - 39

SP - 608

EP - 626

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 2

ER -

Continuity estimates for the Monge - Ampère equation

Abstract

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