Published Paper

Inserted: 31 jul 2025
Last Updated: 5 mar 2026

Journal: Journal of Functional Analysis
Volume: 290
Number: 10
Year: 2025
Doi: 10.1016/j.jfa.2026.111398

Abstract:

This work addresses Faber-Krahn-type inequalities for quantum dot Dirac operators with nonnegative mass on bounded domains in $\mathbb{R}^2$. We show that this family of inequalities is equivalent to a family of Faber-Krahn-type inequalities for $\overline\partial$-Robin Laplacians. Thanks to this, we prove them in the case of simply connected domains for quantum dot boundary conditions asymptotically close to zigzag boundary conditions. Finally, we also study the case of negative mass.