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Eigenstructure of the equilateral triangle, Part II: The Neumann problem

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  • Brian J. McCartin

Abstract

Lame's formulas for the eigenvalues and eigenfunctions of the Laplacian with Neumann boundary conditions on an equilateral triangle are derived using direct elementary mathematical techniques. They are shown to form a complete orthonormal system. Various properties of the spectrum and nodal lines are explored. Implications for related geometries are considered.

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  • Brian J. McCartin, 2002. "Eigenstructure of the equilateral triangle, Part II: The Neumann problem," Mathematical Problems in Engineering, Hindawi, vol. 8, pages 1-23, January.
    • Handle: RePEc:hin:jnlmpe:591873
    DOI: 10.1080/1024123021000053664
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