Geometric origin and some properties of the arctangential heat equation
| Autor: | Yann Brenier |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Physics
Mean curvature flow Minimal surface nonlinear electromagnetism General Mathematics Mathematical analysis Duality (optimization) Nonlinear heat equations 53C44 image processing Nonlinear system mean curvature flow Quadratic equation optimal transport Electromagnetism Minkowski space 35K55 35L65 Heat equation minimal surface equations |
| Zdroj: | Tunisian J. Math. 1, no. 4 (2019), 561-584 |
| Popis: | We establish the geometric origin of the nonlinear heat equation with arctangential nonlinearity: ∂tD=Δ(arctanD) by deriving it, together and in duality 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 a la Otto and its relationship with the Born–Infeld theory of electromagnetism), we briefly discuss its possible use for image processing, once written in nonconservative form and properly discretized. |
| Databáze: | OpenAIRE |
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