Optimal regularity of harmonic maps from a Riemannian manifold into a static Lorentzian manifold
The energy functional for maps from a Riemannian manifold into a static Lorentzian manifold is indefinite. A bounded below functional \({\mathcal F}\) is introduced to be a restriction of the energy. To the minimizing \({\mathcal F}\) maps, the regularity result of Schoen-Uhlenbeck for harmonic maps between Riemannian manifolds is extended. New difficulty comes from the fact that \({\mathcal F}\) is not local.
scientific article; zbMATH DE number 1054049