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On Lebesgue points of entropy solutions to the eikonal equation
Published online by Cambridge University Press: 23 May 2023
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 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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- Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
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