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In mathematics, a (real) Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind. A second-order equation for the unknown function of two variables , is of Monge–Ampère type if ...
蒙日-安培方程（Monge-Ampère Equation）的全面综述，涵盖其背景、发展历史、数学性质、解的性质、应用及当前研究热点，依据资料进行系统性整理并标注引用。 1. 定义与基本背景蒙日-安培方程是一类 二阶完全非线…
西北大学数学学院 开设的偏微分方程与几何分析系列课程包含"Monge-Ampère方程基本理论"专题，由张凯讲授相关内容。 华中师范大学 唐岚副教授于2023年10月23日通过腾讯会议作关于该方程正则性研究的学术报告。 中文名 蒙日一安培方程 外文名 Monge-Ampere equation 所属学科 二阶完全非线性偏微分方程 ...
1 Introduction In this survey we discuss the basic properties of Alexandrov solutions to the Monge-Ampere equation. We then discuss the interior and boundary regularity for Alexandrov solutions to det D2u = 1. At the ...
The Monge-Amp`ere equation is a nonlinear partial differential equation arising in several problems from analysis and geometry, such as the prescribed Gaussian curvature equation, affine geometry, optimal transportation, etc.
基于Monge-Ampère方程模型的实际应用背景,本文主要讨论一类Monge-Ampère 方程的Dirichlet 问题,运用Krasnosel’skii-Precup不动点定理得到了其径向解存在的充分条件。
The Monge–Amp`ere equation has been studied for a long time and is stillacenterofintensiveinterestnowadaysbecauseofitssignificantrolein manyimportantproblemsinanalysis,geometry,physics,partialdifferential equations,anda...
