Eigenstructure of the equilateral triangle. III: The Robin problem (Q1774702)

Summary: Lamé's formulas for the eigenvalues and eigenfunctions of the Laplacian on an equilateral triangle under Dirichlet and Neumann boundary conditions are herein extended to the Robin boundary condition. They are shown to form a complete orthonormal system. Various properties of the spectrum and modal functions are explored. Parts I, II, see SIAM Rev. 45, No. 2, 267--287 (2003; Zbl 1122.35311), Math. Probl. Eng. 8, No. 6, 517--539 (2002; Zbl 1122.35312).