A MULTIPHASE SHAPE OPTIMIZATION PROBLEM FOR EIGENVALUES: QUALITATIVE STUDY AND NUMERICAL RESULTS

被引：13

作者：

Bogosel, Beniamin ^{[1
]}

Velichkov, Bozhidar ^{[2
]}

机构：

[1] Univ Savoie, Lab Math LAMA, F-73376 Le Bourget Du Lac, France

[2] Univ Grenoble 1, Lab Jean Kuntzmann, F-38041 Grenoble 09, France

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2016年 / 54卷 / 01期

关键词：

shape optimization; multiphase; eigenvalues; optimal partition; OPTIMAL PARTITION PROBLEM; NODAL DOMAINS; REGULARITY; EXISTENCE;

D O I：

10.1137/140976406

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In thie paper we consider the following multiphase shape optimization problem min {Sigma(h)(i-1) lambda(1)(Omega(i)) + alpha vertical bar Omega(i)vertical bar : Omega(i) open, Omega(i) subset of D, Omega(i) boolean AND Omega(j) = (sic) where alpha > 0 is a given constant and D subset of R-2 is a bounded open set with Lipschitz boundary. We give some new results concerning the qualitative properties of the optimal sets and the regularity of the corresponding eigenfunctions. We also provide numerical results for the optimal partitions.

引用

页码：210 / 241

页数：32

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