On the spectrum of the negative Laplacian for general doubly-connected bounded domains.
Zayed, E.M.E., Younis, A.I. (1995)
International Journal of Mathematics and Mathematical Sciences
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Zayed, E.M.E., Younis, A.I. (1995)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Zayed, E.M.E. (1993)
International Journal of Mathematics and Mathematical Sciences
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Zayed, E.M.E. (1990)
International Journal of Mathematics and Mathematical Sciences
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Serguei Nazarov, Jan Sokołowski (2008)
Control and Cybernetics
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E. M. E. Zayed (2000)
Collectanea Mathematica
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Serguei A. Nazarov (2002)
Mathematica Bohemica
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It is proved that the first eigenfunction of the mixed boundary-value problem for the Laplacian in a thin domain is localized either at the whole lateral surface of the domain, or at a point of , while the eigenfunction decays exponentially inside . Other effects, attributed to the high-frequency range of the spectrum, are discussed for eigenfunctions of the mixed boundary-value and Neumann problems, too.
Zayed, E.M.E. (1996)
International Journal of Mathematics and Mathematical Sciences
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