International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 13-16, Pages 807-825
doi:10.1155/S0161171204306125
Eigenstructure of the equilateral triangle. III: The Robin problem
Brian J. McCartin
Department of Applied Mathematics, Kettering University, 1700 West Third Avenue, Flint 48504-4898, MI, USA
Abstract
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.