A variational formulation for Dirac operators in bounded domains: applications to spectral geometric inequalities

Antunes, Pedro R. S.; Benguria, Rafael; Lotoreichik, Vladimir; Ourmières-Bonafos, Thomas

http://hdl.handle.net/10400.2/10710

Use this identifier to reference this record.

Name:	Description:	Size:	Format:
2021CMP.pdf		1.19 MB	Adobe PDF	Download

Send Feedback

Authors

Antunes, Pedro R. S.

Benguria, Rafael

Lotoreichik, Vladimir

Ourmières-Bonafos, Thomas

Abstract(s)

We 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.