On the regularity of Dirac eigenfunctions

TL;DR

This paper proves the regularity of Dirac eigenfunctions under MIT boundary conditions across various geometric domains, including smooth, convex polygons, half-space, and bounded domains in 2D and 3D.

Contribution

It provides rigorous proofs of Dirac eigenfunction regularity for a wide range of boundary conditions and domain geometries, extending existing theoretical understanding.

Findings

Eigenfunctions are regular on smooth domains.

Eigenfunctions exhibit regularity on convex polygons.

Results apply to half-space and smooth bounded 3D domains.

Abstract

The article provides proofs for the regularity of Dirac eigenfunctions, subject to MIT boundary conditions employed on various types of open sets ranging from smooth ones to convex polygons in two dimensions, as well as on half-space and smooth bounded domains in three-dimensional space.