Antunes, Pedro R. S.Benguria, RafaelLotoreichik, VladimirOurmières-Bonafos, Thomas2021-05-072021-05-0720210010-3616 (Print)1432-0916 (Online)http://hdl.handle.net/10400.2/10710We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of $\mathbb{R}^2$. Motivated by spectral geometric inequalities, we prove a non-linear variational formulation to characterize its principal eigenvalue. This characterization turns out to be very robust and allows for a simple proof of a Szeg\"o type inequality as well as a new reformulation of a Faber-Krahn type inequality for this operator. The paper is complemented with strong numerical evidences supporting the existence of a Faber-Krahn type inequality.engjournal article