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 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.

References in corpus (1)

• Characterization of minimizers of Aviles-Giga functionals in special domains

Cited by in corpus (1)

• Jumps in Besov spaces and fine properties of Besov and fractional Sobolev functions