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Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle. (English) Zbl 0940.35059

A boundary value problem for the Laplace equation with Dirichlet and Neumann boundary conditions on an equilateral triangle is transformed to a problem of the same type on a rectangle. This enables us to use, e.g., the cyclic reduction method for computing the numerical solution of the problem. By the same transformation, explicit formulae for all eigenvalues and all eigenfunctions of the corresponding operator are obtained.
Reviewer: Jan Zítko (Praha)

MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
65Z05 Applications to the sciences
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References:

[1] Křížek, M., Neittaanmäki, P.: Finite Element Approximaton of Variational Problems and Applications. Longman Scientific & Technical, Harlow, 1990. · Zbl 0708.65106
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