The maximum principle and the Dirichlet problem for Dirac-harmonic maps
Qun Chen, Jürgen Jost,and Guofang Wang
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Submission date: 23. Mar. 2012
published in: Calculus of variations and partial differential equations, 47 (2012) 1/2, p. 87-116
DOI number (of the published article): 10.1007/s00526-012-0512-5
MSC-Numbers: 58E20, 53C27
Keywords and phrases: Dirac-harmonic map, maximum principle, uniqueness, existence
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We establish a maximum principle and uniqueness for Dirac-harmonic maps from a Riemannian spin manifold with boundary into a regular ball in any Riemannian manifold N. Then we prove an existence theorem for a boundary value problem for Dirac-harmonic maps.