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 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.
On Lebesgue points of entropy solutions to the eikonal equation
Marconi E.
2023
Abstract
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 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.
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