Calculus of Variations and Partial Differential Equations

, Volume 47, Issue 1, pp 87–116

The maximum principle and the Dirichlet problem for Dirac-harmonic maps

Open AccessArticle

DOI: 10.1007/s00526-012-0512-5

Cite this article as:
Chen, Q., Jost, J. & Wang, G. Calc. Var. (2013) 47: 87. doi:10.1007/s00526-012-0512-5

Abstract

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.

Keywords

Dirac-harmonic mapMaximum principleUniquenessExistence

Mathematics Subject Classification

Primary 58E20Secondary 53C27
Download to read the full article text

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanPeople’s Republic of China
  2. 2.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  3. 3.Department of Mathematics and Computer ScienceUniversity of LeipzigLeipzigGermany
  4. 4.Institute of MathematicsUniversity FreiburgFreibrugGermany