Abstract
We consider an elliptic system in a half-cylinder ℝ+ × ω with coefficients constant in the direction of the axis and not necessarily smooth. We take different boundary conditions on {0} × ω and Dirichlet condition on {0}×ω. This defines a self-adjoint operatorA D. The main result in this paper is thatA D does not have eigenvalues. This answers conjecture 1.6 raised in [3]. When ω is bounded, we use this result to prove the completeness of a part of the family of eigenvectors, and associated vectors, of a corresponding operator pencils.
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This work was supported by INRIA, France, and partially by UCLA.
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Bouhennache, T. Point spectrum of elliptic operators in fibered half-cylinders and the related completeness problem. Integr equ oper theory 39, 182–192 (2001). https://doi.org/10.1007/BF01195816
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DOI: https://doi.org/10.1007/BF01195816