Nonlinear Sciences > Chaotic Dynamics
[Submitted on 7 Oct 2009 (v1), last revised 14 Mar 2010 (this version, v3)]
Title:The Monge-Ampere equation: various forms and numerical methods
View PDFAbstract:We present three novel forms of the Monge-Ampere 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-Ampere 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-Ampere equation is a sum of such distributions.
Submission history
From: Vladislav Zheligovsky A. [view email][v1] Wed, 7 Oct 2009 15:55:50 UTC (519 KB)
[v2] Thu, 24 Dec 2009 16:57:06 UTC (299 KB)
[v3] Sun, 14 Mar 2010 11:03:50 UTC (302 KB)
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