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A regularizing property of the 2D-eikonal equation


De Lellis, Camillo; Ignat, Radu (2015). A regularizing property of the 2D-eikonal equation. Communications in Partial Differential Equations, 40(8):1543-1557.

Abstract

We prove that any 2-dimensional solution $\psi \in \mathit{W}^{1+^{1}_{3},3}_\mathit{loc}$ of the eikonal equation has locally Lipschitz gradient $\nabla$$\psi$ except at a locally finite number of vortex-points. A related regularizing effect is also obtained for general solutions of the Burgers’ equation.

Abstract

We prove that any 2-dimensional solution $\psi \in \mathit{W}^{1+^{1}_{3},3}_\mathit{loc}$ of the eikonal equation has locally Lipschitz gradient $\nabla$$\psi$ except at a locally finite number of vortex-points. A related regularizing effect is also obtained for general solutions of the Burgers’ equation.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:3 August 2015
Deposited On:27 Jan 2016 11:35
Last Modified:08 Dec 2017 15:55
Publisher:Taylor & Francis
ISSN:0360-5302
Publisher DOI:https://doi.org/10.1080/03605302.2014.999939

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