5 papers
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.
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.
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.
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 $\min\{μ_k(Ω):Ω\mbox{ convex},Ω\subset D, \}$…
Some universal inequalities of eigenvalues and upper bounds for the norm of eigenfunctions of the Laplacian
Kei Funano
In this short survey, we derive some weyl-type universal inequalities of eigenvalues of the Laplacian on a closed Riemannian manifold of nonnegative Ricci curvature. We also give u…