Title A regularizing property of the 2d-eikonal equation Publication Type Journal Article Year of Publication 2015 Authors De Lellis C., Ignat R. Journal Communications in Partial Differential Equations Volume 40 Pagination 1543–1557 Date Published August Publisher Taylor & Francis Type of Article scalar ISSN 0360-5302 Abstract We prove that any 2-dimensional solution \$\backslashpsi \backslashin \backslashmathit{W}\^ {1+\^ {1}_{3},3}_\backslashmathit{loc}\ of the eikonal equation has locally Lipschitz gradient \$\backslash$nabla\$\\backslash$psi\$ except at a locally finite number of vortex-points. A related regularizing effect is also obtained for general solutions of the Burgers? equation. Notes Comm. Partial Differential Equations 40 (2015), no. 8, 1543–1557. URL https://www.tandfonline.com/doi/full/10.1080/03605302.2014.999939 DOI 10.1080/03605302.2014.999939
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