18 citations · 22 across the 21 of their papers we have counts for
5 papers · 1 filter
Inequalities between Dirichlet and Neumann eigenvalues on Carnot groups
Rupert L. Frank, Bernard Helffer, Ari Laptev
We show that the -th Dirichlet eigenvalue of the sub-Laplacian on an open set of a Carnot group is greater than the -st Neumann eigenvalue. This extends earlier results i…
Spectral asymptotics for Robin Laplacians on Lipschitz sets
Rupert L. Frank, Simon Larson
We prove two-term spectral asymptotics for the Riesz means of the eigenvalues of the Laplacian on a Lipschitz domain with Robin boundary conditions. The second term is the same as…
Semiclassical inequalities for Dirichlet and Neumann Laplacians on convex domains
Rupert L. Frank, Simon Larson
We are interested in inequalities that bound the Riesz means of the eigenvalues of the Dirichlet and Neumann Laplacians in terms of their semiclassical counterpart. We show that th…
Riesz means asymptotics for Dirichlet and Neumann Laplacians on Lipschitz domains
Rupert L. Frank, Simon Larson
We consider the eigenvalues of the Dirichlet and Neumann Laplacians on a bounded domain with Lipschitz boundary and prove two-term asymptotics for their Riesz means of arbitrary po…
On Courant and Pleijel theorems for sub-Riemannian Laplacians
Rupert L. Frank, Bernard Helffer
We are interested in the number of nodal domains of eigenfunctions of sub-Laplacians on sub-Riemannian manifolds. Specifically, we investigate the validity of Pleijel's theorem, wh…