Browsing by Author "Antunes, Pedro R. S."

Now showing 1 - 1 of 1
  • No Thumbnail Available
    Item
    A Variational Formulation for Dirac Operators in Bounded Domains. Applications to Spectral Geometric Inequalities
    (2021) Antunes, Pedro R. S.; Benguria, Rafael D.; Lotoreichik, Vladimir; Ourmieres-Bonafos, Thomas
    We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of 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 Szego 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.