Affiliation:
1. Departamento de Matemática Universidade Federal de São Carlos, UFSCar São Carlos Brazil
Abstract
Let
be a broken sheared waveguide; that is,
is built by translating a cross‐section (an arbitrary bounded connected open set of
) in a constant direction along a broken line in
. We prove that the discrete spectrum of the Dirichlet Laplacian operator in
is non‐empty and finite. Furthermore, we show a particular geometry for
, which implies that the total multiplicity of the discrete spectrum is equal to 1.
Funder
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior