Abstract
In the paper, we obtain explicit formulas for the set of eigenvalues and eigenfunctions of the Laplace operator in an arbitrary triangle with different boundary conditions. The paper presents new results in the spectral theory, which are of practical interest in the analysis of vibrations of triangular membranes.
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F. C. A. Pockels, Über die partielle Differentialgleichung ∆u + k 2 u = 0 und deren Auftreten in der matematischen Physik, Mit einem Vorwort von Felix Klein, B. G. Teubner, Leipzig (1891).
B. J. McCartin, “Eigenstructure of the discrete Laplacian on the equilateral triangle: The Dirichlet and Neumann problems,” Applied Mathematical Sciences, Vol. 4, No. 53–56, 2633–2646 (2010).
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Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2019, pp. 61–70.
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Prikazchikov, V.G. Discrete Spectrum of the Laplace Operator for an Arbitrary Triangle with Different Boundary Conditions. Cybern Syst Anal 55, 570–580 (2019). https://doi.org/10.1007/s10559-019-00166-z
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DOI: https://doi.org/10.1007/s10559-019-00166-z