Twisted waveguide with a Neumann window

Abstract : This paper is concerned with the study of the existence/non-existence of the discrete spectrum of the Laplace operator on a domain of $\mathbb R ^3$ which consists in a twisted tube. This operator is defined by means of mixed boundary conditions. Here we impose Neumann Boundary conditions on a bounded open subset of the boundary of the domain (the Neumann window) and Dirichlet boundary conditions elsewhere.
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Philippe Briet, Hiba Hammedi. Twisted waveguide with a Neumann window. Functional Analysis and Operator Theory for Quantum Physics : The Pavel Exner Anniversary Volume, European Mathematical Society, pp.161-175, 2017, EMS Series of Congress Reports, 978-3-03719-175-0. ⟨10.4171/175-1/8⟩. ⟨hal-01264262v3⟩

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