An example of non-convex minimization and an application to Newton's problem of the body of least resistance

DOI10.1016/S0294-1449(00)00062-7zbMath0993.49002OpenAlexW2121930035MaRDI QIDQ5936378

Mark Adriaan Peletier, Thomas Lachand-Robert

Publication date: 2 July 2001

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_2001__18_2_179_0

zbMATH Keywords

body of minimal resistancenon-convex minimization

Mathematics Subject Classification ID

Regularity of solutions in optimal control (49N60) Existence theories for free problems in two or more independent variables (49J10)

Related Items (14)

Local properties of the surface measure of convex bodies ⋮ Regularity in shape optimization under convexity constraint ⋮ Newton's Problem of the Body of Minimal Resistance in the Class of Convex Developable Functions ⋮ The analytical solution of Newton’s aerodynamic problem in the class of bodies with vertical plane of symmetry and developable side boundary ⋮ Partially overdetermined elliptic boundary value problems ⋮ An iterated projection approach to variational problems under generalized convexity constraints ⋮ The problem of the body of revolution of minimal resistance ⋮ Minimizing sequences in class-qualified deposit problems ⋮ Hessian measures in the aerodynamic Newton problem ⋮ Two-dimensional body of maximum mean resistance ⋮ Euler's optimal profile problem ⋮ Non-optimality of conical parts for Newton's problem of minimal resistance in the class of convex bodies and the limiting case of infinite height ⋮ Billiards and two-dimensional problems of optimal resistance ⋮ Method of nose stretching in Newton’s problem of minimal resistance

Cites Work

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• Nearly all convex bodies are smooth and strictly convex
• Newton's Problem of the Body of Minimal Resistance in the Class of Convex Developable Functions
• Extremal points of a functional on the set of convex functions
• What is the Subdifferential of the Closed Convex Hull of a Function?
• Minimum Problems over Sets of Concave Functions and Related Questions
• A symmetry problem in the calculus of variations

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