A regularizing property of the 2D-eikonal equation

We prove that any 2-dimensional solution ψ ∈ W 1+ 1 3,3 loc of the eikonal equation has locally Lipschitz gradient ∇ψ except at a locally finite number of vortex-points. A related regularizing effect is also obtained for general solutions of the Burgers’ equation. DOI: https://doi.org/10.1080/03605302.2014.999939 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-116673 Accepted Version Originally published at: De Lellis, Camillo; Ignat, Radu (2015). A regularizing property of the 2D-eikonal equation. Communications in Partial Differential Equations, 40(8):1543-1557. DOI: https://doi.org/10.1080/03605302.2014.999939 A regularizing property of the 2D-eikonal equation Camillo De Lellis ∗ Radu Ignat † September 1, 2014 Abstract We prove that any 2-dimensional solution ψ ∈ W 1+ 1 3 ,3 loc of the eikonal equation has locally Lipschitz gradient ∇ψ except at a locally finite number of vortices.We prove that any 2-dimensional solution ψ ∈ W 1+ 1 3 ,3 loc of the eikonal equation has locally Lipschitz gradient ∇ψ except at a locally finite number of vortices.