On Lebesgue points of entropy solutions to the eikonal equation
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 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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