Existence of the discrete spectrum in the Fichera layers and crosses of arbitrary dimension

Abstract

We describe the Dirichlet spectrum structure for the Fichera layers and crosses in any dimension $n\ge 3$. Also the application of the obtained results to the classical Brownian exit times problem in these domains.

22 pages, 4 figures

References in corpus (3)

• Eigenvalue inequalities and absence of threshold resonances for waveguide junctions
• Dirichlet spectrum of the Fichera layer
• Discrete spectrum of interactions concentrated near conical surfaces