Self-adjoint Extensions for the Neumann Laplacian and Applications

被引：0

作者：

S.A.NAZAROV ^{[1
]}

J.SOKOLOWSKI ^{[2
]}

机构：

[1] Institute of Mechanical Engineering Problems V.O.Bolshoy pr.61,199178 St Petersburg Russia

[2] Institut Elie Cartan Laboratoire de Mathématiques Université Henri Poincaré NancyI B.P.239 54506 Vandoeuvrelès Nancy Cedex France and Systems Research Institute of the Polish Academy of Sciences ul.Newelska601-447Warszawa Poland

来源：

Acta Mathematica Sinica,English Series | 2006年 / 22卷 / 03期

关键词：

shape optimization; asymptotic expansions; self-adjoint extension; weighted spaces with detached asymptotics; topological derivatives;

D O I：

暂无

中图分类号：

O175.8 [边值问题];

学科分类号：

070104 ;

摘要：

A new technique is proposed for the analysis of shape optimization problems.The techniqueuses the asymptotic analysis of boundary value problems in singularly perturbed geometrical domains.The asymptotics of solutions are derived in the framework of compound and matched asymptoticsexpansions.The analysis involves the so-called interior topology variations.The asymptotic expansionsare derived for a model problem,however the technique applies to general elliptic boundary valueproblems.The self-adjoint extensions of elliptic operators and the weighted spaces with detachedasymptotics are exploited for the modelling of problems with small defects in geometrical domains.The error estimates for proposed approximations of shape functionals are provided.

引用

页码：879 / 906

页数：28

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