The spectrum of a weighted Laplacian in the half‐space
Tahar Z. Boulmezaoud, Nabil Kerdid · Mathematical Methods in the Applied Sciences · 2015
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 © 2015 John Wiley & Sons, Ltd.