Newton's problem of the body of minimal resistance under a single-impact assumption

被引：35

作者：

Comte, M ^{[1
]}

Lachand-Robert, T ^{[1
]}

机构：

[1] Univ Paris 06, Anal Numer Lab, F-75252 Paris 05, France

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2001年 / 12卷 / 02期

关键词：

Local Minimizer; Geometrical Property; Unit Disc; Radial Function; Minimal Resistance;

D O I：

10.1007/PL00009911

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the problem of the body of minimal resistance as formulated in [2]. Sect. 5: minimize F(u) := integral (u) dx/(1 + /delu(x)/(2)), where Omega is the unit disc of R-2, in the class of radial functions u : Omega --> [0,M] satisfying a geometrical property (I), corresponding to a single-impact assumption (M > 0 is a given parameter). We prove the existence of a critical value M* of M. For M greater than or equal to M*, there exist a unique local minimizer of the functional. For M < M*, the set of local minimizers is not compact in H-1, though they all achieve the same value of the functional.

引用

页码：173 / 211

页数：39

共 8 条

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