We consider the magnetic Dirichlet Laplacian with constant magnetic field on domains of
finite measure. First, in the case of a disk, we prove that the eigenvalue branches with …

We study the classical problem of finding asymptotics for the Bessel functions J ν (z) and Y ν
(z) as the argument z and the order ν approach infinity. We use blow-up analysis to find …

We prove explicit uniform two-sided bounds for the phase functions of Bessel functions and
their derivatives. As a consequence, we obtain new enclosures for the zeros of Bessel …

We provide bounds for the sequence of eigenvalues {λ i (Ω)} i of the Dirichlet problem (I− Δ)
ln u= λ u in Ω, u= 0 in RN\Ω, where (I− Δ) ln is the Klein-Gordon operator with Fourier …

We show the existence of classes of non-tiling domains satisfying Pólya's conjecture in any
dimension, in both the Euclidean and non-Euclidean cases. This is a consequence of a …

In this paper we study optimization problems for Neumann eigenvalues among convex
domains with a constraint on the diameter or the perimeter. We work mainly in the plane …

We present numerical minimizers for the first seven eigenvalues of the magnetic Dirichlet
Laplacian with constant magnetic field in a wide range of field strengths. Adapting an …

Denote by NN (Ω, λ) N_\calN(Ω,λ) the counting function of the spectrum of the Neumann
problem in the domain Ω Ω on the plane. G. Pólya conjectured that NN (Ω, λ)⩾(4 π)− 1| Ω| λ …

We are interested in inequalities that bound the Riesz means of the eigenvalues of the
Dirichlet and Neumann Laplaciancs in terms of their semiclassical counterpart. We show …

Given a convex domain and a convex subdomain, we prove a variant of domain
monotonicity for the Neumann eigenvalues of the Laplacian. As an application of our …