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Generalized linear elasticity in exterior domains. II: low‐frequency asymptotics
Author(s) -
Weck Norbert,
Witsch Karl J.
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19971125)20:17<1501::aid-mma936>3.0.co;2-8
Subject(s) - mathematics , elasticity (physics) , degenerate energy levels , spherical harmonics , homogeneous , mathematical analysis , operator (biology) , linear elasticity , neumann series , pure mathematics , finite element method , combinatorics , physics , biochemistry , chemistry , repressor , quantum mechanics , gene , transcription factor , thermodynamics
Abstract We continue the study of the operators of generalized linear elasticity and investigate the behaviour of the solutions as the frequency tends to zero. We identify degenerate operators in terms of special solutions to the static problem which must be added to the usual Neumann series in order to describe the low frequency behaviour adequately. As a byproduct we construct solutions to the homogeneous static operator (‘spherical elastics’) which generalize the spherical harmonics and give rise to a ‘spherical elastics expansion’. © 1997 B. G. Teubner Stuttgart‐John Wiley & Sons Ltd.