Jul 6 – 8, 2022
Institut de Mathématiques de Bordeaux
Europe/Paris timezone

Fabio Pizzichillo: Boundary value problems for 2-D Dirac operator on Corner domains and the Coulomb interaction.

Jul 7, 2022, 10:30 AM
1h
Salle de Conférences (Institut de Mathématiques de Bordeaux)

Salle de Conférences

Institut de Mathématiques de Bordeaux

351 cours de la libération 33400 TALENCE

Description

This talk aims to present results on the self-adjoint extensions of Dirac operators on plane domains with corners in dimension two. We consider the case of infinite-mass boundary conditions and we obtain explicitly the self-adjoint extensions of the operator. It turns out that the presence of corners typically spoils the elliptic regularity known to hold for smooth boundaries.

Then we discuss the self-adjointness and some spectral properties of these operators in presence of a Coulomb-type potential with the singularity placed on the vertex.

This is a collaboration work with Hanne Van Den Bosch, Biagio Cassano and Matteo Gallone.

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