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A Rellich type theorem for the Helmholtz equation in a conical domain

Anne-Sophie Bonnet-Ben Dhia 1 Sonia Fliss 1 Christophe Hazard 1 Antoine Tonnoir 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : We prove that there cannot exist square-integrable nonzero solutions to the Helmholtz equation in an axisymmetric conical domain whose vertex angle is greater than π. This implies in particular the absence of eigenvalues embedded in the essential spectrum of a large class of partial differential operators which coincide with the Laplacian in the conical domain.
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Submitted on : Thursday, June 4, 2015 - 5:41:52 PM
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Anne-Sophie Bonnet-Ben Dhia, Sonia Fliss, Christophe Hazard, Antoine Tonnoir. A Rellich type theorem for the Helmholtz equation in a conical domain. Comptes Rendus Mathématique, Elsevier Masson, 2015, ⟨10.1016/j.crma.2015.10.015⟩. ⟨hal-01160242⟩



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