The distance function in the presence of an obstacle
| Autor: | Paolo Albano, Vincenzo Basco, Piermarco Cannarsa |
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| Přispěvatelé: | Albano P., Basco V., Cannarsa P. |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Popis: | We study the Riemannian distance function from a fixed point (a point-wise target) of Euclidean space in the presence of a compact obstacle bounded by a smooth hypersurface. First, we show that such a function is locally semiconcave with a fractional modulus of order one half and that, near the obstacle, this regularity is optimal. Then, in the Euclidean setting, we prove that the singularities of the distance function propagate, in the sense that each singular point belongs to a nontrivial singular continuum. Finally, we investigate the lack of differentiability of the distance function when a convex obstacle is present. 31 pages, 4 figures, original article |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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