Twisted waveguide with a Neumann window

TL;DR

This paper investigates the spectral properties of the Laplace operator on a twisted waveguide with mixed boundary conditions, focusing on the existence of discrete spectrum influenced by a Neumann window.

Contribution

It provides new insights into how the Neumann window affects the existence or non-existence of discrete spectrum in twisted waveguides.

Findings

Discrete spectrum existence depends on the size and position of the Neumann window.

Conditions for non-existence of discrete spectrum are established.

Results contribute to understanding wave propagation in twisted structures.

Abstract

This paper is concerned with the study of theexistence/non-existence of the discrete spectrum of the Laplaceoperator on a domain of $\mathbb R ^3$ which consists in atwisted tube. This operator is defined by means of mixed boundaryconditions. Here we impose Neumann Boundary conditions on abounded open subset of the boundary of the domain (the Neumannwindow) and Dirichlet boundary conditions elsewhere.