Eigenstructure of the equilateral triangle. II: The Neumann problem (Q1432039)

Summary: Lame's formulas for the eigenvalues and eigenfunctions of the Laplacian with Neumann boundary conditions on an equilateral triangle are derived using direct elementary mathematical techniques. They are shown to form a complete orthonormal system. Various properties of the spectrum and nodal lines are explored. Implications for related geometries are considered. Part I, cf. SIAM Rev. 45, No. 2, 267--287 (2003; Zbl 1122.35311), Part III, see Int. J. Math. Math. Sci. 2004, No. 13--16, 807--825 (2004; Zbl 1123.35008).