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

2020/06/22 by F. L. Bakharev, Bakharev, F. L., Alexander I. Nazarov +1 · 2 citations
Mathematics · #Spectral Theory in Mathematical Physics #Stochastic processes and statistical mechanics #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2006.12045

Abstract

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

Cited by

• Survival probability for jump processes in unbounded domains on metric measure spaces
• Monotonicity of discrete spectra of Dirichlet Laplacian in 3-dimensional layers

Related

• The multifractal spectrum of Brownian intersection local times
• Bounds for exit times of Brownian motion and the first Dirichlet eigenvalue for the Laplacian
• Two simple topics in spectral theory
• A spectral approach to the narrow escape problem in the disk
• Spectrum of the Laplacian with mixed boundary conditions in a chamfered quarter of layer