Publications de Luigi Provenzano

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

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

Eigenvalues of elliptic operators with density

Luigi Provenzano, Bruno Colbois

2018