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math.AP2026
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…
math.AP2024
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…
math.AP2024
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…