Optimal Roughening of Convex Bodies

Canadian Journal of Mathematics

Alexander Plakhov¹ 

DOI  :  10.4153/CJM-2011-070-9

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

A body moves in a rarefied medium composed of point particles atrest. The particles make elastic reflections when colliding with thebody surface, and do not interact with each other. We consider ageneralization of Newton's minimal resistance problem: given twobounded convex bodies $C_1$ and $C_2$ such that $C_1 subset C_2subset mathbb{R}^3$ and $partial C_1 cap partial C_2 = emptyset$, minimize theresistance in the class of connected bodies $B$ such that $C_1 subsetB subset C_2$. We prove that the infimum of resistance is zero; thatis, there exist "almost perfectly streamlined" bodies.

【 授权许可】

Unknown