Proves that the eigenvalue index shift Ψ(d,1,Ω) between Neumann and Dirichlet Laplacians is at least C(e/2)^d for any bounded domain Ω, and the same bound holds for all k when Ω is convex.
Hatcher,Geometric inequalities between Dirichlet and Neumann eigen- values, preprint
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Two universal inequalities are established for Dirichlet eigenvalues of the Laplacian on Euclidean convex domains.
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Inequalities between Dirichlet and Neumann eigenvalues in large dimensions
Proves that the eigenvalue index shift Ψ(d,1,Ω) between Neumann and Dirichlet Laplacians is at least C(e/2)^d for any bounded domain Ω, and the same bound holds for all k when Ω is convex.
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Some universal inequalities for Dirichlet eigenvalues of the Laplacian on a Euclidean convex domain
Two universal inequalities are established for Dirichlet eigenvalues of the Laplacian on Euclidean convex domains.