Open Access
2017 Symmetry and Solutions to the Helmholtz Equation Inside an Equilateral Triangle
Nathaniel Stambaugh, Mark Semon
J. Geom. Symmetry Phys. 43: 37-45 (2017). DOI: 10.7546/jgsp-43-2017-37-45


Solutions to the Helmholtz equation within an equilateral triangle which solve either the Dirichlet or Neumann problem are investigated. This is done by introducing a pair of differential operators, derived from symmetry considerations, which demonstrate interesting relationships among these solutions. One of these operators preserves the boundary condition while generating an orthogonal solution and the other leads to a bijection between solutions of the Dirichlet and Neumann problems.


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Nathaniel Stambaugh. Mark Semon. "Symmetry and Solutions to the Helmholtz Equation Inside an Equilateral Triangle." J. Geom. Symmetry Phys. 43 37 - 45, 2017.


Published: 2017
First available in Project Euclid: 12 May 2017

zbMATH: 1371.35038
MathSciNet: MR3644813
Digital Object Identifier: 10.7546/jgsp-43-2017-37-45

Primary: 35J05
Secondary: 35B06

Keywords: Dirichlet and Neumann problems , equilateral triangle , Helmholtz equation , Laplacian

Rights: Copyright © 2017 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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