8 papers
An asymptotic shape optimization problem for Riesz means of Laplacian eigenvalues
Rupert L. Frank, Simon Larson
We review our recent results on the problem of optimizing Riesz means of Laplace eigenvalues among convex sets of given measure in the regime where the cut-off parameter in the def…
Optimizing Riesz means of Robin Laplace operators on cuboids in a semiclassical limit
Matthias Baur, Simon Larson
We study asymptotic shape optimization for Riesz means of Robin Laplacian eigenvalues among cuboids of fixed measure. Our focus is the regime where the Robin parameter is proportio…
Uniform bounds for Neumann heat kernels and their traces in convex sets
Rupert L. Frank, Simon Larson
We prove a bound on the heat trace of the Neumann Laplacian on a convex domain that captures the first two terms in its small-time expansion, but is valid for all times and depends…
Improved semiclassical eigenvalue estimates for the Laplacian and the Landau Hamiltonian
Rupert L. Frank, Simon Larson, Paul Pfeiffer
The Berezin--Li--Yau and the Kröger inequalities show that Riesz means of order of the eigenvalues of the Laplacian on a domain of finite measure are bounded in term…
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…