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arXiv · 1312.2516

Analysis of polarity

Shiri Artstein-Avidan·Yanir A. Rubinstein
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Abstract

We develop a differential theory for the polarity transform parallel to that for the Legendre transform, which is applicable when the functions studied are "geometric convex", namely convex, non-negative and vanish at the origin. This analysis may be used to solve a family of first order equations reminiscent of Hamilton--Jacobi and conservation law equations, as well as some second order Monge-Ampere type equations. A special case of the latter, that we refer to as the homogeneous polar Monge--Ampere equation, gives rise to a canonical method of interpolating between convex functions.

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Shiri Artstein-Avidan, Yanir A. Rubinstein. 2013-12-09. Analysis of polarity. https://doi.org/10.1007/s11854-017-0016-5

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