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Laplace operator; boundary value problem; eigenvalues; eigenfunctions
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.
[1] Křížek, M., Neittaanmäki, P.: Finite Element Approximaton of Variational Problems and Applications. Longman Scientific & Technical, Harlow, 1990. MR 1066462
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