A connection between quantum dot Dirac operators and $\overline{\partial }$-Robin Laplacians in the context of shape optimization problems

Joaquim Duran, Albert Mas, Tomás Sanz-Perela

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 inequaliti…