Journal Articles Tunisian Journal of Mathematics Year : 2019

Geometric origin and few properties of the arctangential heat equation

Abstract

We establish the geometric origin ot the nonlinear heat equation with arct-angential nonlinearity: ∂ t D = ∆(arctan D) by deriving it, together and in du-ality with the mean curvature flow equation, from the minimal surface equation in Minkowski space-time, through a suitable quadratic change of time. After examining various properties of the arctangential heat equation (in particular through its optimal transport interpretation à la Otto and its relationship with the Born-Infeld theory of Electromagnetism), we shortly discuss its possible use for image processing, once written in non-conservative form and properly discretized.
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Dates and versions

hal-01740320 , version 1 (21-03-2018)

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Yann Brenier. Geometric origin and few properties of the arctangential heat equation. Tunisian Journal of Mathematics, 2019, 1 (4), pp.561-584. ⟨10.2140/tunis.2019.1.561⟩. ⟨hal-01740320⟩
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