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http://hdl.handle.net/10773/35431
Title: | On the structure of singular points of a solution to Newton’s least resistance problem |
Author: | Plakhov, Alexander |
Keywords: | Newton’s problem of least resistance Convex geometry Singular points of a convex body |
Issue Date: | 21-Sep-2022 |
Publisher: | Springer |
Abstract: | We consider the following problem stated in 1993 by Buttazzo and Kawohl (Math Intell 15:7–12, 1993): minimize the functional ∫∫ Ω(1 + |∇u(x, y)|^2)^{−1}dxdy in the class of concave functions u : Ω → [0,M], where Ω ⊂ ℝ^2 is a convex domain and M >0. It generalizes the classical minimization problem, which was initially stated by I. Newton in 1687 in the more restricted class of radial functions. The problem is not solved until now; there is even nothing known about the structure of singular points of a solution. In this paper we, frst, solve a family of auxiliary 2D least resistance problems and, second, apply the obtained results to study singular points of a solution to our original problem. More precisely, we derive a necessary condition for a point being a ridge singular point of a solution and prove, in particular, that all ridge singular points with horizontal edge lie on the top level and zero level sets. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/35431 |
DOI: | 10.1007/s10883-022-09616-y |
ISSN: | 1079-2724 |
Publisher Version: | https://link.springer.com/article/10.1007/s10883-022-09616-y |
Appears in Collections: | CIDMA - Artigos OGTCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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2022 JDCS.pdf | 1.89 MB | Adobe PDF | View/Open |
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