3 papers
math-ph2022
A Block-diagonal form for four-component operators describing Graphene Quantum Dots
Rafael D. Benguria, Edgardo Stockmeyer, Cristóbal Vallejos +1
We consider four-component Dirac operators on domains in the plane. With suitable boundary conditions, these operators describe graphene quantum dots. The most general boundary con…
math-ph2018
Existence and non-existence of minimizers for Poincaré-Sobolev inequalities
Rafael D. Benguria, Cristóbal Vallejos, Hanne Van Den Bosch
In this paper we study the existence and non-existence of minimizers for a type of (critical) Poincaré-Sobolev inequalities. We show that minimizers do exist for smooth domains in…
math-ph2018
Gagliardo-Nirenberg-Sobolev inequalities for convex domains in
Rafael D. Benguria, Cristobal Vallejos, Hanne Van Den Bosch
A special type of Gagliardo-Nirenberg-Sobolev (GNS) inequalities in has played a key role in several proofs of Lieb-Thirring inequalities. Recently, a need for GNS i…