The boundary value problem for Dirac-harmonic maps (Q1949972)

The authors study Dirac-harmonic maps from a Riemannian surface to an arbitrary compact Riemannian manifold. It is shown that a weakly Dirac-harmonic map is smooth in the interior of the domain. The regularity results for Dirac-harmonic maps are also proved at the boundary when they solve an appropriate boundary value problem which is the mathematical interpretation of the D-branes of superstring theory.