The spectrum of a weighted Laplacian in the half-space

Abstract : J. Banasiak In this paper, we deal with spectral properties of a weighted Laplacian in the half-space when a Dirichlet or a Neumann boundary condition is imposed. After proving that the spectrum is discrete under suitable assumptions, we give explicit formulae of eigenvalues and eigenfunctions in a specific case. In particular, the obtained eigenfunctions are rational or pseudo-rational and have remarkable orthogonality properties. These results suggest the use of the discovered functions for approximating solutions of elliptic problems in the half-space. Copyright (c) 2015John Wiley and Sons, Ltd.
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Tahar Zamene Boulmezaoud, Nabil Kerdid. The spectrum of a weighted Laplacian in the half-space. Mathematical Methods in the Applied Sciences, Wiley, 2016, 39 (2), pp.280-288. ⟨10.1002/mma.3476⟩. ⟨hal-02166369⟩

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