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

TL;DR

This paper investigates the Dirichlet spectrum of Fichera layers and crosses in any dimension, providing insights into their spectral structure and applications to Brownian exit times.

Contribution

It characterizes the Dirichlet spectrum for Fichera layers and crosses in arbitrary dimensions, extending previous results to higher-dimensional domains.

Findings

Spectral structure of Fichera layers and crosses described.

Application to Brownian exit times established.

Results valid for any dimension n ≥ 3.

Abstract

We describe the Dirichlet spectrum structure for the Fichera layers and crosses in any dimension $n\ge3$. Also the application of the obtained results to the classical Brownian exit times problem in these domains.