[BibTeX]

*Preprint*

**Inserted:** 2 sep 2014

**Last Updated:** 16 dec 2014

**Journal:** CPDE

**Year:** 2014

**Links:**
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**Abstract:**

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.