Problems of Minimal Resistance and the Kakeya Problem

DOI10.1137/15M1012931zbMath1343.49072OpenAlexW1073429343MaRDI QIDQ2808257

Alexander Plakhov

Publication date: 20 May 2016

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1012931

zbMATH Keywords

shape optimizationminimal resistanceNewton's problemKakeya problem

Mathematics Subject Classification ID

Optimization of shapes other than minimal surfaces (49Q10) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Related Items (6)

A solution to Newton's least resistance problem is uniquely defined by its singular set ⋮ On the structure of singular points of a solution to Newton's least resistance problem ⋮ Rotating rod and ball ⋮ Billiard in a rotating half-plane ⋮ A note on Newton's problem of minimal resistance for convex bodies ⋮ Method of nose stretching in Newton’s problem of minimal resistance

Cites Work

• On Newton's problem of minimal resistance
• Variational methods in shape optimization problems
• The multiplier problem for the ball
• Newton's Problem of the Body of Minimal Resistance in the Class of Convex Developable Functions
• Newton’s problem of minimal resistance under the single-impact assumption
• Comment on “Functions and Domains Having Minimal Resistance Under a Single-Impact Assumption”[SIAM J. Math. Anal., 34 (2002), pp. 101–120]
• Functions and Domains Having Minimal Resistance Under a Single-Impact Assumption
• Minimum Problems over Sets of Concave Functions and Related Questions
• Minimizing within Convex Bodies Using a Convex Hull Method
• The Kakeya Problem for Simply Connected and for Star-Shaped Sets
• The Kakeya Problem
• A symmetry problem in the calculus of variations
• Existence of minimizers for Newtons's problem of the body of minimal resistance under a single impact assumption
• Newton's problem of the body of minimal resistance under a single-impact assumption
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