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- W4295537331 abstract "We study the regularity of the Euclidean distance function from a given point-wise target of a n-dimensional vector space in the presence of a compact obstacle bounded by a smooth hypersurface. It is known that such a function is semiconcave with fractional modulus one half. We provide a geometrical explanation of the exponent one half. Furthermore, under a natural (weak) assumption on the position of the point-wise target relatively to the obstacle, we show that there exists a point in the boundary of the obstacle so that no better regularity result holds near such a point. As a consequence of this result, we show that the Euclidean metric cannot be extended to a tubular neighborhood of the obstacle, as a Riemannian metric, keeping the property that the associated distances coincide outside the obstacle." @default.
- W4295537331 created "2022-09-14" @default.
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- W4295537331 date "2023-02-01" @default.
- W4295537331 modified "2023-09-27" @default.
- W4295537331 title "On the regularity of the distance near the boundary of an obstacle" @default.
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- W4295537331 doi "https://doi.org/10.1016/j.jmaa.2022.126680" @default.
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