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Generalized linear elasticity in exterior domains. I: Radiation problems
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<1469::aid-mma935>3.0.co;2-l
Subject(s) - mathematics , eigenvalues and eigenvectors , sobolev space , mathematical analysis , infinity , boundary value problem , elasticity (physics) , helmholtz equation , pure mathematics , physics , materials science , quantum mechanics , composite material
We use Hodge–Helmholtz decompositions of weighted Sobolev spaces to solve time‐harmonic exterior‐boundary value problems for perturbations of the ( a δ d + bd δ)‐system (δ: the co‐differential, a , b >0). We prove, that a Fredholm alternative holds true, the eigensolutions decay polynomially at infinity, and that the positive eigenvalues do not accumulate. © 1997 B. G. Teubner Stuttgart‐John Wiley & Sons Ltd.