33 citations · 75 across the 13 of their papers we have counts for
13 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 relativistic Hardy-type inequality with minimisers
Luca Fanelli, Fabio Pizzichillo
In this paper, we prove a sharp, weighted Hardy-type inequality for the Dirac operator. A key feature of our result is that the inequality is not only sharp but also attained, and…
Dirac operators with infinite mass boundary conditions on unbounded domains with infinite corners
Miguel Camarasa, Fabio Pizzichillo
We investigate the self-adjointness of the two dimensional Dirac operator with infinite mass boundary conditions on an unbounded domain with an infinite number of corners. We prove…
Keller and Lieb-Thirring estimates of the eigenvalues in the gap of Dirac operators
Jean Dolbeault, David Gontier, Fabio Pizzichillo +1
We estimate the lowest eigenvalue in the gap of the essential spectrum of a Dirac operator with mass in terms of a Lebesgue norm of the potential. Such a bound is the counterpart f…
Dirac-Coulomb Operators with Infinite Mass Boundary Conditions in Sectors
Biagio Cassano, Matteo Gallone, Fabio Pizzichillo
We investigate the properties of self-adjointness of a two-dimensional Dirac operator on an infinite sector with infinite mass boundary conditions and in presence of a Coulomb-type…
Dirac operators and shell interactions: a survey
Thomas Ourmières-Bonafos, Fabio Pizzichillo
In this survey we gather recent results on Dirac operators coupled with -shell interactions. We start by discussing recent advances regarding the question of self-adjointness fo…