Abstract
The main goal of this paper is to characterize the weak limits of sequences of smooth maps from a Riemannian manifold intoS 1. This is achieved in terms of Cartesian currents. Applications to the existence of minimizers of area type functionals in the class of maps with values inS 1 satisfying Dirchlet and homological conditions are then discussed. The so called dipole problem is solved, too.
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This work has been partially supported by the Ministero dell'Universitá e della Ricerca Scientifica, by C.N.R. contract n. 91.01343.CT01, and by the European Research Project GADGET. It was partially carried out while the first and the third author were visiting the Mathematisches Institut der Universität Bonn under the support respectively of the Alexander von Humboldt-Stiftung and of the SBF 256.
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Giaquinta, M., Modica, G. & Souček, J. Variational problems for maps of bounded variation with values inS 1 . Calc. Var 1, 87–121 (1993). https://doi.org/10.1007/BF02163266
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DOI: https://doi.org/10.1007/BF02163266