26 citations · 44 across the 14 of their papers we have counts for
10 papers · 1 filter
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…
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…
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…
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…
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…
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…
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…