Inserted: 15 nov 2022
Last Updated: 15 nov 2022
We consider entropy solutions to the eikonal equation $\vert\nabla u \vert =1$ in two space dimensions. These solutions are motivated by a class of variational problems and fail in general to have bounded variation. Nevertheless they share with BV functions, several of their fine properties: we show in particular that the set of non-Lebesgue points has co-dimension at least one.