Prikazchikov V.G.
Discrete spectrum of the Laplace operator for an arbitrary triangle with different boundary conditions

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. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: Dirichlet and Neumann boundary conditions, Laplace operator, spectrum, triangle, Eigenvalues and eigenfunctions, Laplace transforms, Vibration analysis, Different boundary condition, Dirichlet and Neumann boundary conditions, Discrete spectrum, Explicit formula, Laplace operator, Spectral theory, spectrum, triangle, Boundary conditions

Cite:
Prikazchikov V.G. (2019). Discrete spectrum of the Laplace operator for an arbitrary triangle with different boundary conditions. Cybernetics and Systems Analysis, 55 (4), 61-70. doi: https://doi.org/10.1007/s10559-019-00166-z http://jnas.nbuv.gov.ua/article/UJRN-0001003094 [In Russian].