Asymptotische Eigenwertverteilung des Laplace-Operators in bestimmten unbeschränkten Gebieten mit Neumannschen Randbedingungen und Restgliedabschätzungen

Abstract

In the paper, the distribution of the eigenvalues of the Laplacian is investigated in some unbounded domains of ${\mathbb{R}}^n$ with Neumann boundary conditions. For certain domains asymptotic formulas with remainder estimates are established. The capital term of the asymptotic coincides in this case with the asymptotic formula of the Laplacian in bounded domains.