1 citations · 2 across the 9 of their papers we have counts for
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Robin counting functions on cuboids in the critical scaling regime
Matthias Baur, Simon Larson
We consider eigenvalue counting functions of Robin Laplace operators on cuboids where the Robin parameter and the spectral cut-off are coupled. Our main focus is the critical r…
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…