De Lellis, Camillo; Ignat, Radu (2015). A regularizing property of the 2D-eikonal equation. Communications in Partial Differential Equations, 40(8):1543-1557.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Analysis
Physical Sciences > Applied Mathematics |
| Language: | English |
| Date: | 3 August 2015 |
| Deposited On: | 27 Jan 2016 11:35 |
| Last Modified: | 14 Nov 2023 02:47 |
| Publisher: | Taylor & Francis |
| ISSN: | 0360-5302 |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.1080/03605302.2014.999939 |
| Project Information: |
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De Lellis, Camillo