26 citations · 44 across the 14 of their papers we have counts for
17 papers
Relativistic Virial Operators
Lucrezia Cossetti, Luca Fanelli, Fabio Pizzichillo
When studying Dirac operators, it is well known that the phenomenon of Zitterbewegung leads to a lack of convexity of the variance, which creates difficulties in the analysis of di…
A unified approach to Hardy-type inequalities with Bessel pairs
Lucrezia Cossetti, Lorenzo D'Arca
In this paper, we provide suitable characterisations of pairs of weights known as Bessel pairs, that ensure the validity of weighted Hardy-type inequalities. The abstract…
On the point spectrum of electromagnetic Dirac operators
Naiara Arrizabalaga, Lucrezia Cossetti, Matias Morales
In this work, we develop the method of multipliers for electromagnetic Dirac operators and establish sufficient conditions on the magnetic and electric fields that guarantee the ab…
Error bounds for Physics Informed Neural Networks in Nonlinear Schrödinger equations placed on unbounded domains
Miguel Á. Alejo, Lucrezia Cossetti, Luca Fanelli +2
We consider the subcritical nonlinear Schrödinger (NLS) in dimension one posed on the unbounded real line. Several previous works have considered the deep neural network approximat…
The virial theorem and the method of multipliers in spectral theory
Lucrezia Cossetti, David Krejcirik
We provide a link between the virial theorem in functional analysis and the method of multipliers in theory of partial differential equations. After giving a physical insight into…
Uniform resolvent estimates and absence of eigenvalues of biharmonic operators with complex potentials
Lucrezia Cossetti, Luca Fanelli, David Krejcirik
We quantify the subcriticality of the bilaplacian in dimensions greater than four by providing explicit repulsivity/smallness conditions on complex additive perturbations under whi…
On uniqueness of solutions to the surface electromigration equation
Lucrezia Cossetti, Luca Fanelli, Felipe Linares
In this paper we investigate on uniqueness properties of solutions to the surface electromigration (SEM) equation, which is a generalisation of the more classical Zakharov-Kuznetso…
Spectral enclosures for the damped elastic wave equation
Biagio Cassano, Lucrezia Cossetti, Luca Fanelli
In this paper we investigate spectral properties of the damped elastic wave equation. Deducing a correspondence between the eigenvalue problem of this model and the one of Lamé ope…
Improved Hardy-Rellich inequalities
Biagio Cassano, Lucrezia Cossetti, Luca Fanelli
We investigate Hardy-Rellich inequalities for perturbed Laplacians. In particular, we show that a non-trivial angular perturbation of the free operator typically improves the inequ…
Eigenvalue bounds and spectral stability of Lamé operators with complex potentials
Biagio Cassano, Lucrezia Cossetti, Luca Fanelli
This paper is devoted to providing quantitative bounds on the location of eigenvalues, both discrete and embedded, of non self-adjoint Lamé operators of elasticity in…
A limiting absorption principle for Helmholtz systems and time-harmonic isotropic Maxwell's equations
Lucrezia Cossetti, Rainer Mandel
In this work we investigate the L^p-L^q-mapping properties of the resolvent associated with the time-harmonic isotropic Maxwell operator. As spectral parameters close to the spectr…
Absence of eigenvalues of Dirac and Pauli Hamiltonians via the method of multipliers
Lucrezia Cossetti, Luca Fanelli, David Krejcirik
By developing the method of multipliers, we establish sufficient conditions on the magnetic field and the complex, matrix-valued electric potential, which guarantee that the corres…
On the unique continuation property of solutions to the two-dimensional Zakharov-Kuznetsov equation
Lucrezia Cossetti
The purpose of the current paper is twofold: to some extent it is intended as a review of the recent optimal result in [4] concerning the unique continuation property of solutions…
Bounds on eigenvalues of perturbed Lamé operators with complex potentials
Lucrezia Cossetti
Several recent papers have focused their attention in proving the correct analogue to the Lieb-Thirring inequalities for non self-adjoint operators and in finding bounds on the dis…
Absence of eigenvalues of non-self-adjoint Robin Laplacians on the half-space
Lucrezia Cossetti, David Krejcirik
By developing the method of multipliers, we establish sufficient conditions which guarantee the total absence of eigenvalues of the Laplacian in the half-space, subject to variable…
Uniqueness results for Zakharov-Kuznetsov equation
Lucrezia Cossetti, Luca Fanelli, Felipe Linares
In this paper we study uniqueness properties of solutions to the Zakharov-Kuznetsov equation of plasma physic. Given two sufficiently regular solutions we prove that, i…
Uniform resolvent estimates and absence of eigenvalues for Lamé operators with potentials
Lucrezia Cossetti
We consider the -order perturbed Lamé operator . It is well known that if one considers the free case, namely the spectrum of is purely continuo…