| Self-adjoint Extensions for the Neumann Laplacian and Applications |
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| 作者姓名： | S. A. NAZAROV J. SOKOLOWSKI |
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| 作者单位： | [1]Institute of Mechanical Engineering Problems, V. O. Bolshoy pr. 61, 199178 St Petersburg, Russia [2]Institut Elie Cartan, Laboratoire de Mathématiques, Université Henri Poincard Nancy I, B. P. 239, 54506 Vandoeuvre lès Nancy Cedex, France, and Systems Research Institute of the Polish Academy of Sciences, ul. Newelska 6, 01-447 Warszawa, Poland |
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| 基金项目： | Partially supported by INRIA in the framework of the grant 00-01 from institut franco-russe A. M. Liapunov d＇informatique et de math6matiques appliquées and by the grant 4 T11A 01524 of the State Committee for the Scientific Research of the Republic of Poland. The paper was prepared during a visit of S. A. Nazarov to the Institute Elie Carton in Nancy |
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| 摘 要： |
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| 关 键 词： | 外形最优化 渐近扩展 自伴随矩阵扩展 加权空间 渐近分离 |
| 收稿时间： | 16 March 2004 |
| 修稿时间： | 2004-03-162005-06-28 |
Self–adjoint Extensions for the Neumann Laplacian and Applications |
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| S. A. NAZAROV J. SOKOLOWSKI.Self-adjoint Extensions for the Neumann Laplacian and Applications[J].Acta Mathematica Sinica,2006,22(3):879-906. |
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| Authors: | S A Nazarov J Soko?owski |
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| Institution: | (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 Nancy I, 239, 54506 Vandoeuvre lés Nancy Cedex, France;(3) Systems Research Institute of the Polish Academy of Sciences, ul. Newelska 6, 01-447 Warszawa, Poland |
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| Abstract: | A new technique is proposed for the analysis of shape optimization problems. The technique uses 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 asymptotics expansions. The analysis involves the so-called interior topology variations. The asymptotic expansions are derived for a model problem, however the technique applies to general elliptic boundary value problems. The self-adjoint extensions of elliptic operators and the weighted spaces with detached asymptotics are exploited for the modelling of problems with small defects in geometrical domains, The error estimates for proposed approximations of shape functionals are provided. |
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| Keywords: | shape optimization asymptotic expansions self-adjoint extension weighted spaces with detached asymptotics topological derivatives |
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