Geodesic
Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle
Applications of Mathematics, Tome 43 (1998) no. 4, pp. 311-320 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.1023/A:1023269922178
Classification : 35J05, 35P10, 65Z05
Keywords: Laplace operator; boundary value problem; eigenvalues; eigenfunctions 
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     title = {Eigenvalues and eigenfunctions of the {Laplace} operator on an equilateral triangle},
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     year = {1998},
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Práger, Milan. Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle. Applications of Mathematics, Tome 43 (1998) no. 4, pp. 311-320. doi: 10.1023/A:1023269922178

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