Loading...
1 results
Search Results
Now showing 1 - 1 of 1
- A variational formulation for Dirac operators in bounded domains: applications to spectral geometric inequalitiesPublication . Antunes, Pedro R. S.; Benguria, Rafael; Lotoreichik, Vladimir; Ourmières-Bonafos, ThomasWe 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.