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• W1968202227 endingPage "983" @default.
• W1968202227 startingPage "941" @default.
• W1968202227 abstract "Asymptotic expansions are constructed for the eigenvalues of the Dirichlet problem for the biharmonic operator in a domain with highly indented and rapidly oscillating boundary (the Kirchhoff model of a thin plate). The asymptotic constructions depend heavily on the quantity $gamma$ that describes the depth $O(varepsilon ^gamma )$ of irregularity ($varepsilon$ is the oscillation period). The resulting formulas relate the eigenvalues in domains with close irregular boundaries and make it possible, in particular, to control the order of perturbation and to find conditions ensuring the validity (or violation) of the classical Hadamard formula." @default.
• W1968202227 created "2016-06-24" @default.
• W1968202227 creator A5078134916 @default.
• W1968202227 creator A5079716919 @default.
• W1968202227 date "2011-12-01" @default.
• W1968202227 modified "2023-10-18" @default.
• W1968202227 title "The spectrum asymptotics for the Dirichlet problem in the case of the biharmonic operator in a domain with highly indented boundary" @default.
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• W1968202227 doi "https://doi.org/10.1090/s1061-0022-2011-01178-1" @default.
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