Asymptotics of Eigenvalues of a Plate with Small Clamped Zone |
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| Authors: | Campbell Alain Nazarov Sergueï A |
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| Institution: | (1) Laboratoire de Mécanique Modélisation Mathématique et Numérique, Université de Caen, BP 5186, 14032 Caen Cedex, France;(2) Laboratory of Mathematical Methods in Solid Mechanics, N.I.I.M.M., Saint-Petersburg University, Russia |
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| Abstract: | Different types of asymptotic expansions are constructed and justified for eigenvalues of the Dirichlet problem for the biharmonic operator in a plane domain with a small hole   of the diameter (the Kirchhoff-Love plate clamped at ). Depending on properties of an eigenfunction of the limiting problem, the expansions happen either to be series in powers of , or to contain terms, holomorphic in | ln |–1 |
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| Keywords: | asymptotic expansions biharmonic operator holomorphy Sobolev problem spectral problem outer and inner expansions weighted Sobolev spaces |
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