Abstract
We study the regularity of harmonic maps from Riemannian manifold into a static Lorentzian manifold. We show that when the domain manifold is two-dimensional, any weakly harmonic map is smooth. We also show that when dimension n of the domain manifold is greater than two, there exists a weakly harmonic map for the Dirichlet problem which is smooth except for a closed set whose (n − 2)-dimensional Hausdorff measure is zero.
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