Note on a paper of E. M. E. Zayed and S. F. M. Ibraham.
Eberhard, W., Freiling, G., Schneider, A. (1992)
International Journal of Mathematics and Mathematical Sciences
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Eberhard, W., Freiling, G., Schneider, A. (1992)
International Journal of Mathematics and Mathematical Sciences
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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.
Nazarov, Serguei A.
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Andrianov, I.V., Awrejcewicz, J., Ivankov, A. (2005)
Mathematical Problems in Engineering
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O. A. Olejnik (1989)
Journées équations aux dérivées partielles
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