## Integrability by compensation for Dirac equation

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- by Francesca Da Lio, Tristan Rivière and Jerome Wettstein PDF
- Trans. Amer. Math. Soc.
**375**(2022), 4477-4511 Request permission

## Abstract:

We consider the Dirac operator acting on the Clifford algebra ${C\ell }_{m}$. 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. $\epsilon -$regularity theorem). This extends in 4 space dimension as well as in 3 dimension a similar result obtained previously by the two first authors in 2D in F. Da Lio and T. Riviére [*Critical chirality in elliptic systems*, Ann. Inst. H. Poincare Anal. Non Linéaire,

**38**(2021), no. 5, 1373–1405].

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## Additional Information

**Francesca Da Lio**- Affiliation: Department of Mathematics, ETH Zentrum, CH-8093 Zürich, Switzerland
- MR Author ID: 627699
**Tristan Rivière**- Affiliation: Department of Mathematics, ETH Zentrum, CH-8093 Zürich, Switzerland
- ORCID: 0000-0002-5676-8401
**Jerome Wettstein**- Affiliation: Department of Mathematics, ETH Zentrum, CH-8093 Zürich, Switzerland
- MR Author ID: 1449865
- ORCID: 0000-0002-0756-279X
- Received by editor(s): September 28, 2021
- Received by editor(s) in revised form: January 11, 2022
- Published electronically: March 31, 2022
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**375**(2022), 4477-4511 - MSC (2020): Primary 35J46, 35B65, 81Q05
- DOI: https://doi.org/10.1090/tran/8656
- MathSciNet review: 4419066