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

Tarp-Ficenc, Ulrike
August 2005
Calculus of Variations & Partial Differential Equations;Aug2005, Vol. 23 Issue 4, p451
Academic Journal
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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