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Volume 55 >>> № 4 JULY — AUGUST 2019

UDC 519.63

V.G. Prikazchikov¹

¹ Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

DISCRETE SPECTRUM OF THE LAPLACE OPERATOR FOR
AN ARBITRARY TRIANGLE WITH DIFFERENT BOUNDARY-VALUE CONDITIONS

Abstract. In the paper, we obtain the explicit formulas for a 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 the vibrations of triangular membranes .

Keywords: spectrum, Laplace operator, triangle, Dirichlet�s and Neumann�s boundary conditions.

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REFERENCES

Pockels F.C.A. die partielle Differentialgleichung und deren Auftreten in der matematischen Physik. Mit einem Vorwort von Felix Klein. Leipzig: B.G. Teubner, 1891. 364 �.

McCartin B.J. Eigenstructure of the discrete Laplacian on the equilateral triangle: The Dirichlet and Neumann problems. Applied Mathematical Sciences. 2010. Vol. 4, N 53. P. 2633�2646.

UDC 519.63

DISCRETE SPECTRUM OF THE LAPLACE OPERATOR FOR AN ARBITRARY TRIANGLE WITH DIFFERENT BOUNDARY-VALUE CONDITIONS

REFERENCES

DISCRETE SPECTRUM OF THE LAPLACE OPERATOR FOR
AN ARBITRARY TRIANGLE WITH DIFFERENT BOUNDARY-VALUE CONDITIONS