Publications de Joachim Stubbe

Semiclassical Estimates for Eigenvalue Means of Laplacians on Spheres

Joachim Stubbe, Luigi Provenzano, Paolo Luzzini, Davide Buoso

We compute three-term semiclassical asymptotic expansions of counting functions and Riesz-means of the eigenvalues of the Laplacian on spheres and hemispheres, for both Dirichlet and Neumann boundary conditions. Specifically for Riesz-means we prove upper ...

SPRINGER2023

The first Grushin eigenvalue on cartesian product domains

Joachim Stubbe, Luigi Provenzano, Paolo Luzzini

In this paper, we consider the first eigenvalue.1(O) of the Grushin operator.G :=.x1 + |x1|2s.x2 with Dirichlet boundary conditions on a bounded domain O of Rd = R d1+ d2. We prove that.1(O) admits a unique minimizer in the class of domains with prescribed ...

WALTER DE GRUYTER GMBH2023

Two-term, asymptotically sharp estimates for eigenvalue means of the Laplacian (Retraction of Vol 8, Pg 1529, 2018)

Joachim Stubbe

2021

On the spectral asymptotics for the buckling problem

Joachim Stubbe, Luigi Provenzano

We provide a direct proof of Weyl's law for the buckling eigenvalues of the biharmonic operator on domains of Rd of finite measure. The proof relies on asymptotically sharp lower and upper bounds that we develop for the Riesz mean R-2(z). Lower bounds are ...

AIP Publishing2021

Complementary Asymptotically Sharp Estimates for Eigenvalue Means of Laplacians

Joachim Stubbe, Luigi Provenzano

We present asymptotically sharp inequalities, containing a 2nd term, for the Dirichlet and Neumann eigenvalues of the Laplacian on a domain, which are complementary to the familiar Berezin-Li-Yau and Kroger inequalities in the limit as the eigenvalues tend ...

OXFORD UNIV PRESS2021

Weyl-type bounds for Steklov eigenvalues

Joachim Stubbe, Luigi Provenzano

We present upper and lower bounds for Steklov eigenvalues for domains in RN+1 with C-2 boundary compatible with the Weyl asymptotics. In particular, we obtain sharp upper bounds on Riesz-means and the trace of corresponding Steklov heat kernel. The key res ...

EUROPEAN MATHEMATICAL SOC2019

Two-term, asymptotically sharp estimates for eigenvalue means of the Laplacian

Joachim Stubbe

We present asymptotically sharp inequalities for the eigenvalues mu(k) of the Laplacian on a domain with Neumann boundary conditions, using the averaged variational principle introduced in [14]. For the Riesz mean R-1(z) of the eigenvalues we improve the k ...

EUROPEAN MATHEMATICAL SOC2018

On sums of eigenvalues of elliptic operators on manifolds

Joachim Stubbe

We use the averaged variational principle introduced in a recent article on graph spectra [10] to obtain upper bounds for sums of eigenvalues of several partial differential operators of interest in geometric analysis, which are analogues of Kroger's bound ...

European Mathematical Soc2017

On sums of graph eigenvalues (vol 455, pg 168, 2014)

Joachim Stubbe

Elsevier Science Inc2014

On sums of graph eigenvalues

Joachim Stubbe

We use two variational techniques to prove upper bounds for sums of the lowest several eigenvalues of matrices associated with finite, simple, combinatorial graphs. These include estimates for the adjacency matrix of a graph and for both the standard combi ...

Elsevier Science Inc2014