The Monge-Ampère equation: Various forms and numerical solution

Zheligovsky V.; Podvigina O.; Frisch U.

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The Monge-Ampère equation: Various forms and numerical solution

机译：Monge-Ampère方程：各种形式和数值解

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We present three novel forms of the Monge-Ampère equation, which is used, e.g., in image processing and in reconstruction of mass transportation in the primordial Universe. The central role in this paper is played by our Fourier integral form, for which we establish positivity and sharp bound properties of the kernels. This is the basis for the development of a new method for solving numerically the space-periodic Monge-Ampère problem in an odd-dimensional space. Convergence is illustrated for a test problem of cosmological type, in which a Gaussian distribution of matter is assumed in each localised object, and the right-hand side of the Monge-Ampère equation is a sum of such distributions.

机译：我们介绍了Monge-Ampère方程的三种新颖形式，该形式用于例如图像处理以及原始宇宙中大众运输的重构。本文的核心作用是我们的傅里叶积分形式，为此我们建立了内核的正性和尖锐束缚性质。这是开发一种新方法的基础，该方法可以对奇数维空间中的空间周期Monge-Ampère问题进行数值求解。举例说明了宇宙学类型的测试问题的收敛性，其中假设在每个局部物体中都存在高斯分布，而Monge-Ampère方程的右侧是这些分布的总和。

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《Journal of Computational Physics》 |2010年第13期|共19页
作者
Zheligovsky V.; Podvigina O.; Frisch U.;
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正文语种 eng
中图分类数学物理方法;
关键词
Iterative methods; Monge-Ampère equation; Numerical solution;

机译：迭代方法Monge-Ampère方程数值解;

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1. The Monge-Ampère equation: Various forms and numerical solution [J] . Zheligovsky V., Podvigina O., Frisch U. Journal of Computational Physics . 2010,第13期

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The Monge-Ampère equation: Various forms and numerical solution

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