# zbMATH — the first resource for mathematics

$$A$$-harmonic equations and the Dirac operator. (English) Zbl 1207.35144
Summary: We show how $$A$$-harmonic equations arise as components of Dirac systems. We generalize $$A$$-harmonic equations to $$A$$-Dirac equations. Removability theorems are proved for solutions to $$A$$-Dirac equations.

##### MSC:
 35J60 Nonlinear elliptic equations 35Q40 PDEs in connection with quantum mechanics 30G30 Other generalizations of analytic functions (including abstract-valued functions) 35B45 A priori estimates in context of PDEs
Full Text:
##### References:
 [1] Abreu-Blaya, R; Bory-Reyes, J; Peña-Peña, D, Jump problem and removable singularities for monogenic functions, The Journal of Geometric Analysis, 17, 1-13, (2007) · Zbl 1211.30056 [2] Chen, Q; Jost, J; Li, J; Wang, G, Dirac-harmonic maps, Mathematische Zeitschrift, 254, 409-432, (2006) · Zbl 1103.53033 [3] Chen, Q; Jost, J; Li, J; Wang, G, Regularity theorems and energy identities for Dirac-harmonic maps, Mathematische Zeitschrift, 251, 61-84, (2005) · Zbl 1091.53042 [4] Chen, Q; Jost, J; Wang, G, Nonlinear Dirac equations on Riemann surfaces, Annals of Global Analysis and Geometry, 33, 253-270, (2008) · Zbl 1141.58011 [5] Wang C: A remark on nonlinear Dirac equations. preprint preprint · Zbl 0845.35015 [6] Wang C, Xu D: Regularity of Dirac-harmonic maps. International Mathematics Research Notices 2009, (20):3759-3792. · Zbl 1182.58007 [7] Heinonen J, Kilpeläinen T, Martio O: Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Mathematical Monographs. Oxford University Press, New York, NY, USA; 1993:vi+363. · Zbl 0780.31001 [8] Nolder, CA; Ryan, J, Dirac operators, Advances in Applied Clifford Algebra, 19, 391-402, (2009) · Zbl 1170.53028 [9] Nolder CA: Nonlinear -Dirac equations. to appear in Advances in Applied Clifford Algebra to appear in Advances in Applied Clifford Algebra · Zbl 1091.53042 [10] Kaufman, R; Wu, JM, Removable singularities for analytic or subharmonic functions, Arkiv för Matematik, 18, 107-116, (1980) · Zbl 0444.30002 [11] Koskela, P; Martio, O, Removability theorems for solutions of degenerate elliptic partial differential equations, Arkiv för Matematik, 31, 339-353, (1993) · Zbl 0845.35015 [12] Kilpeläinen, T; Zhong, X, Removable sets for continuous solutions of quasilinear elliptic equations, Proceedings of the American Mathematical Society, 130, 1681-1688, (2002) · Zbl 1027.35032 [13] Meyers, NG, Mean oscillation over cubes and Hölder continuity, Proceedings of the American Mathematical Society, 15, 717-721, (1964) · Zbl 0129.04002 [14] Langmeyer, N, The quasihyperbolic metric, growth, and John domains, Annales Academiæ Scientiarium Fennicæ. Mathematica, 23, 205-224, (1998) · Zbl 0904.30014 [15] Stein EM: Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, no. 30. Princeton University Press, Princeton, NJ, USA; 1970:xiv+290.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.