Range of the First Three Eigenvalues of the Planar Dirichlet Laplacian
Copyright policy )Range of the First Three Eigenvalues of the Planar Dirichlet Laplacian
AbstractExtensive numerical experiments have been conducted by the authors, aimed at finding the admissible range of the ratios of the first three eigenvalues of a planar Dirichlet Laplacian. The results improve the previously known theoretical estimates of M. Ashbaugh and R. Benguria. Some properties of a maximizer of the ratio λ3/λ1 are also proved in the paper.
- Heriot-Watt University United Kingdom
- Department of Mathematics
Numerical methods for eigenvalue problems for boundary value problems involving PDEs, Numerical Analysis, isoperimetric estimates, a priori estimates, eigenvalues, Estimates of eigenvalues in context of PDEs, Dirichlet Laplacian, Numerical Analysis (math.NA), 35P15 (Primary); 65N25 (Secondary), bounded domain, Spectral Theory, FOS: Mathematics, universal estimates, Spectral Theory (math.SP)
Numerical methods for eigenvalue problems for boundary value problems involving PDEs, Numerical Analysis, isoperimetric estimates, a priori estimates, eigenvalues, Estimates of eigenvalues in context of PDEs, Dirichlet Laplacian, Numerical Analysis (math.NA), 35P15 (Primary); 65N25 (Secondary), bounded domain, Spectral Theory, FOS: Mathematics, universal estimates, Spectral Theory (math.SP)
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