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Stephan Weyers

L^q-solutions to the Cosserat spectrum in bounded and exterior domains

Keywords: Cosserat spectrum, Lamé’s equation

If G ⊂ Rⁿ is a bounded or an exterior domain with sufficiently smooth boundary then for the eigenvalue problem
Δu = λ∇ div u,  u|_∂G = 0
λ = 1 is an eigenvalue of infinite multiplicity and λ = 2 is an accumulation point of eigenvalues of finite multiplicity. For the L^q-solutions corresponding to eigenvalues λ ∈ R\{1,2}, one can prove the existence of higher (classical) derivatives. Furthermore they do not depend on q. As an application we obtain a relationship of Green’s function to the reproducing kernel.

Analysis, Oldenbourg Wissenschaftsverlag

Print ISSN: 0174-4747
Volume: 26, 01/2006
Pages: 085 - 167

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