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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 21, Issue 5


On a shape design problem for one spectral functional

Yusif S. Gasimov
Published Online: 2013-06-06 | DOI: https://doi.org/10.1515/jip-2012-0001


In the work we deal with the eigenvalue problem for the elliptic operator with variable domain. The object under investigation is a functional involving eigenvalues of this operator. A formula for the first variation of the functional with respect to the domain is derived. A necessary condition for the optimal shape is obtained. Evident formulas are given for the eigenvalues in the optimal domain for some particular cases.

Keywords: Shape optimization; eigenvalue problem; support function; domain variation; eigenfrequency

About the article

Received: 2012-01-11

Published Online: 2013-06-06

Published in Print: 2013-10-01

Citation Information: Journal of Inverse and Ill-Posed Problems, Volume 21, Issue 5, Pages 629–637, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jip-2012-0001.

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