Integrability by compensation for Dirac Equation
Analysis of PDEs
2021-08-24 v1
Abstract
We consider the Dirac Operator acting on the Clifford Algebra . We show that under critical assumptions on the potential and the spinor field the equation is subject to an integrability by compensation phenomenon and has a sub-critical behaviour below some positive energy threshold (i.e. regularity theorem). This extends in 4 space dimensions as well as in 3 dimensions a similar result obtained previously by the two first authors in 2 D in \cite{DLR1}.
Keywords
Cite
@article{arxiv.2108.10200,
title = {Integrability by compensation for Dirac Equation},
author = {Francesca Da Lio and Tristan Rivière and Jerome Wettstein},
journal= {arXiv preprint arXiv:2108.10200},
year = {2021}
}