On a shape design problem for one spectral functional
Yusif S. GasimovInstitute of Applied Mathematics Baku State University, Z. Khalilov Str. 23, AZ1148 Baku, Azerbaijan
2013en
ABI
Abstract
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.
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Cited by 20 references