Abstract.
Let \( {\user1{\mathcal{Y}}} \) be a smooth 1-connected compact oriented manifold without boundary, such that its 2-homology group has no torsion. We characterize in any dimension n the weak \( W^{{1,2}} (B^{n} ,{\user1{\mathcal{Y}}}) \) lower semicontinuous envelope of the Dirichlet integral of Sobolev maps in \( W^{{1,2}} (B^{n} ,{\user1{\mathcal{Y}}}) \).
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Received: 6 November 2004, Accepted: 15 November 2004, Published online: 22 December 2004
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Giaquinta, M., Mucci, D. The relaxed Dirichlet energy of mappings into a manifold. Calc. Var. 24, 155–166 (2005). https://doi.org/10.1007/s00526-004-0318-1
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DOI: https://doi.org/10.1007/s00526-004-0318-1