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On a shape design problem for one spectral functional
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Yusif S. Gasimov
Published/Copyright:
June 6, 2013
Abstract.
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
Received: 2012-01-11
Published Online: 2013-06-06
Published in Print: 2013-10-01
© 2013 by Walter de Gruyter Berlin Boston
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- On a shape design problem for one spectral functional
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Keywords for this article
Shape optimization;
eigenvalue problem;
support function;
domain variation;
eigenfrequency
Articles in the same Issue
- Masthead
- Conservation laws in differential geometry of plane curves and for eikonal equation and inverse problems
- On a shape design problem for one spectral functional
- An adjoint method for proving identifiability of coefficients in parabolic equations
- Semismooth Newton and quasi-Newton methods in weighted ℓ1-regularization
- On the iterative inversion of generalized attenuated Radon transforms
