关于Monge-Ampère型方程二阶导数估计的一个注记

IF 2.1 2区数学 Q1 MATHEMATICS

Advanced Nonlinear Studies Pub Date : 2022-04-03 DOI:10.1515/ans-2022-0036

N. Trudinger

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引用次数: 1

摘要

摘要在本文中，我们回顾了N.S.Trudinger、F.Jiang和J.Liu以前对Monge-Ampère型偏微分方程解的Pogorelov型内部和全局二阶导数估计。考虑到Guillen Kitagawa和Rankin最近的严格凸性正则性结果，并遵循我们在最优运输情况下的早期工作，我们在生成的雅可比方程的更一般情况下，以及在随后应用于第二边值问题的经典可解性和全局正则性时，删除了单调性假设。

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A note on second derivative estimates for Monge-Ampère-type equations

Abstract In this article, we revisit previous Pogorelov-type interior and global second derivative estimates of N. S. Trudinger, F. Jiang, and J. Liu for solutions of Monge-Ampère-type partial differential equations. Taking account of recent strict convexity regularity results of Guillen-Kitagawa and Rankin and following our earlier work in the optimal transportation case, we remove the monotonicity assumptions in the more general case of generated Jacobian equations and consequently in the subsequent application to classical solvability and global regularity for second boundary value problems.

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来源期刊

Advanced Nonlinear Studies 数学-数学

CiteScore

3.00

自引率

5.60%

发文量

审稿时长

12 months

期刊介绍： Advanced Nonlinear Studies is aimed at publishing papers on nonlinear problems, particulalry those involving Differential Equations, Dynamical Systems, and related areas. It will also publish novel and interesting applications of these areas to problems in engineering and the sciences. Papers submitted to this journal must contain original, timely, and significant results. Articles will generally, but not always, be published in the order when the final copies were received.