# 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$$\psi except at a locally finite number of vortex-points. A related regularizing effect is also obtained for general solutions of the Burgers’ equation. We prove that any 2-dimensional solution \psi \in \mathit{W}^{1+^{1}_{3},3}_\mathit{loc} of the eikonal equation has locally Lipschitz gradient \nabla$$\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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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 3 August 2015 27 Jan 2016 11:35 05 Apr 2016 19:41 Taylor & Francis 0360-5302 https://doi.org/10.1080/03605302.2014.999939
Permanent URL: https://doi.org/10.5167/uzh-116673

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Language: English
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