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On the minimizers of the relaxed energy functional of mappings from higher dimensional balls into S2

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Abstract.

We prove a new approximation theorem, which enables us to show that the relaxed energy \(\mathcal{F}(u)\) of Sobolev mappings u from higher dimensional balls into S2 is given by \(% F{\left( u \right)}: = E{\left( u \right)} + 4\pi {\text{m}}_{i} {\left( {S_{u} } \right)}% $%, provided their singular set is of Lebesgue measure zero. Here \(% {\text{m}}_{i} {\left( {S_{u} } \right)}% $% is the mass of the minimal integer multiplicity connection associated to the singularity current S u of u. Using this approximation theorem, we prove a partial regularity theorem for minimizers of the relaxed energy functional.

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Correspondence to Ulrike Tarp-Ficenc.

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Received: 5 May 2004, Accepted: 19 October 2004, Published online: 10 December 2004

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Tarp-Ficenc, U. On the minimizers of the relaxed energy functional of mappings from higher dimensional balls into S2. Calc. Var. 23, 451–467 (2005). https://doi.org/10.1007/s00526-004-0310-9

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