Integrability by compensation for Dirac equation

Da Lio, Francesca; Rivière, Tristan; Wettstein, Jerome

doi:10.1090/tran/8656

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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