Calculus of Variations and Geometric Measure Theory

X. Lamy - E. Marconi

On Lebesgue points of entropy solutions to the eikonal equation

created by marconi on 15 Nov 2022

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Preprint

Inserted: 15 nov 2022
Last Updated: 15 nov 2022

Year: 2022

Abstract:

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.


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