On Lebesgue points of entropy solutions to the eikonal equation

Abstract

We consider entropy solutions to the eikonal equation$|\nabla u|=1$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 several of their fine properties with BV functions: we show in particular that the set of non-Lebesgue points has at least one co-dimension.