Calculus of Variations and Geometric Measure Theory

C. De Lellis - R. Ignat

A regularizing property of the 2d-eikonal equation

created by delellis on 02 Sep 2014
modified on 24 May 2017


Published Paper

Inserted: 2 sep 2014
Last Updated: 24 may 2017

Journal: Comm. Partial Differential Equations
Volume: 40
Pages: 1543–1557
Year: 2015
Links: PDF


We prove that any $2$-dimensional solution $\psi\in W_{loc}^{1+\frac 1 3, 3}$ of the eikonal equation has locally Lipschitz gradient $\nabla \psi$ except at a locally finite number of vortices.