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Article Dans Une Revue Proceedings of the Royal Society of Edinburgh: Section A, Mathematics Année : 2023

On Lebesgue points of entropy solutions to the eikonal equation

Xavier Lamy
Elio Marconi

Résumé

We consider entropy solutions to the eikonal equation |∇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.
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Dates et versions

hal-04128802 , version 1 (14-06-2023)

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Xavier Lamy, Elio Marconi. On Lebesgue points of entropy solutions to the eikonal equation. Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, In press, ⟨10.1017/prm.2023.50⟩. ⟨hal-04128802⟩
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