Eigenstructure of the equilateral triangle, Part II: The Neumann problem

By B. McCartin. 2002

73 citations recorded by the source corpus.

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.

Subfields: Biomedical Engineering, Geometry and Topology, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/6a2367edced7ea090ad94db563d0ef686c95da32

Citations in the corpus

• Minimizing Neumann fundamental tones of triangles: An optimal Poincaré inequality (2009, unknown): “iangle were derived two centuries ago by Lam´e, albeit without a proof of completeness. We present the first few modes below. For proofs, see the recent exposition (including completeness) by McCartin [18], building on work of Pr´ager [22]. A different approach is due to Pinsky [20]. Consider the the ”
• Eigenstructure of the equilateral triangle (2003, unknown): “Such a complete, direct, and elementary derivation of Lamé's formulas has only recently been provided for the Dirichlet problem [11] as well as the Neumann problem [9].”