Mapping problems, fundamental groups and defect measures
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Submission date: 17. Nov. 1998
published in: Acta Mathematica Sinica, 15 (1999) 1, p. 25-52
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We study all possible weak limits of a minimizing sequence, for p-energy functionals, consisting of continuous maps between Riemannian manifolds subject to a Dirichlet boundary condition or a homotopy condition. We show that if p is not an integer, then any such weak limit is a strong limit and, in particular, a stationary p-harmonic map which is continuous away from a closed subset of the Hausdorff dimension . If p is an integer, then any such weak limit is a weakly p-harmonic map along with a (n-p)-rectifiable Radon measure . Moreover, the limiting map is continuous away from a closed subset with =0. Finally, we discussed the possible varifolds type theory for Sobolev mappings.