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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 1979, Volume 19, Number 4, Pages 921–936 (Mi zvmmf5351)  
A method of estimating lower bounds for eigenvalues of differential operators by the method of fictitious domains

L. T. Poznyak

Leningrad
Full-text PDF (1792 kB)
Abstract: The Bazley-Fox method of intermediate problems and the method of fictitious domains are used in combination to obtain lower bounds for the eigenvalue of a two-dimensional second-order elliptic equation with Dirichlet boundary condition. It is shown that, with this approach, under very general assumption about the coefficients of the differential equation and the domain in which it is specified, the problem of finding lower bounds for the eigenvalues can be reduced to finding the eigenvalues of a matrix.
Received: 20.01.1977
English version:
USSR Computational Mathematics and Mathematical Physics, 1979, Volume 19, Issue 4, Pages 132–148
DOI: https://doi.org/10.1016/0041-5553(79)90162-9
Bibliographic databases:
Document Type: Article
UDC: 517.988.8
MSC: Primary 35P15; Secondary 35R20, 65N25, 35J15
Language: Russian
Citation: L. T. Poznyak, “A method of estimating lower bounds for eigenvalues of differential operators by the method of fictitious domains”, Zh. Vychisl. Mat. Mat. Fiz., 19:4 (1979), 921–936; U.S.S.R. Comput. Math. Math. Phys., 19:4 (1979), 132–148
Citation in format AMSBIB
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\by L.~T.~Poznyak
\paper A~method of~estimating lower bounds for eigenvalues of~differential operators by~the~method of~fictitious domains
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1979
\vol 19
\issue 4
\pages 921--936
\mathnet{http://mi.mathnet.ru/zvmmf5351}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=544755}
\zmath{https://zbmath.org/?q=an:0419.35065}
\transl
\jour U.S.S.R. Comput. Math. Math. Phys.
\yr 1979
\vol 19
\issue 4
\pages 132--148
\crossref{https://doi.org/10.1016/0041-5553(79)90162-9}
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