On the Structure of Singular Points of a Solution to Newton’s Least Resistance Problem

We consider the following problem stated in 1993 by Buttazzo and Kawohl (Math Intell 15:7–12, 1993): minimize functional $${\int \limits } {\int }_{\Omega (1 + |\nabla u(x,y)|^{2})^{-1} dx dy$$ class of concave functions u : Ω → [0,M], where $${\Omega \subset \mathbb {R}^{2}$$ is a convex domain M > 0. It generalizes classical minimization problem, which was initially I. Newton 1687 more restricted radial functions. The not solved until now; there even nothing known about structure singular points solution. In this paper we, first, solve family auxiliary 2D least resistance problems and, second, apply obtained results to study solution our original problem. More precisely, we derive necessary condition for point being ridge prove, particular, that all with horizontal edge lie on top level zero sets.