On an isoperimetric inequality and various methods for the Bernoulli’s free boundary problems

被引：0
|
作者：
Seck D. [1 ]
机构：
[1] Laboratoire de Mathématique de la Décision et d’Analyse Numérique, FASEG, Université Cheikh Anta Diop de Dakar, BP 16 889, Dakar-Fann
来源：
São Paulo Journal of Mathematical Sciences | 2016年 / 10卷 / 1期
关键词：
Bernoulli’s free boundary problem; Convexity; Eigenvalue; Isoperimetric inequality; Local strict minimum; Shape derivatives; Sufficient conditions; Symmetry;
D O I：
10.1007/s40863-015-0012-6
中图分类号：
学科分类号：
摘要：
This survey paper on the Bernoulli’s free boundary problems, deals with some important questions of geometric analysis of optimal shapes. Isoperimetric inequality is discussed and other geometric qualitative properties such as symmetry and convexity properties. A comparison of diffrent approaches to establish existence solution of the Bernoulli’s free boundary problems is done followed by some questions on spectral geometry, the numerical analysis and the analysis on manifolds of the problems studied. © 2015, Instituto de Matemática e Estatística da Universidade de São Paulo.
引用
收藏
页码：36 / 59
页数：23
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