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Critical chirality in elliptic systems

Institution:	1. Department of Mathematics, Texas A & M University, College Station, TX 77843-3368, USA;2. Department of Mathematics, University of North Carolina - Chapel Hill, Chapel Hill, NC 27599, USA;3. Department of Mathematics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada;1. Politecnico di Torino, Dipartimento di Scienze Matematiche “G.L. Lagrange”, Corso Duca degli Abruzzi, 24, 10129, Torino, Italy;2. CNRS, Sorbonne Université, Inria, Université de Paris, Laboratoire Jacques-Louis Lions, Paris, France;3. Dipartimento di Matematica Tullio Levi-Civita, Università degli Studi di Padova, via Trieste 63, 35131 Padova, Italy;4. Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systèmes, 91190, Gif-sur-Yvette, France;1. Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China;2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Abstract:	We establish the regularity in 2 dimension of $L^{2}$ solutions to critical elliptic systems in divergence form involving chirality operators of finite $W^{1, 2}$ -energy.

Keywords:	Second order elliptic systems Regularity Integrability by compensation Dirac operator Quaternion algebra
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