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math.SP2026
Some universal inequalities for Dirichlet eigenvalues of the Laplacian on a Euclidean convex domain
Kei Funano
We establish two universal inequalities for Dirichlet eigenvalues of the Laplacian on a Euclidean convex domain.
math.SP2026
A note on the distribution of Neumann eigenvalues of the Laplacian on a Euclidean convex domain
Kei Funano
We establish two universal inequalities for Neumann eigenvalues of the Laplacian on a Euclidean convex domain.
math.SP2025
Two new universal inequalities for Neumann eigenvalues of the Laplacian on a planar convex domain
Kei Funano
We establish two new universal inequalities for Neumann eigenvalues of the Laplacian on a planar convex domain.
math.SP2023
Two extremum problems for Neumann eigenvalues
Lorenzo Cavallina, Kei Funano, Antoine Henrot +3
Neumann eigenvalues being non-decreasing with respect to domain inclusion, it makes sense to study the two shape optimization problems $\min\{μ_k(Ω):Ω\mbox{ convex},Ω\subset D, \}$…