Let 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)(Bn, Y) lower semicontinuous envelope of the Dirichlet integral of Sobolev maps in W^(1,2)(Bn, Y).
The relaxed Dirichlet energy of mappings into a manifold / Giaquinta, M; Mucci, Domenico. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 24:2(2005), pp. 155-166. [10.1007/s00526-004-0318-1]
The relaxed Dirichlet energy of mappings into a manifold
MUCCI, Domenico
2005
Abstract
Let 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)(Bn, Y) lower semicontinuous envelope of the Dirichlet integral of Sobolev maps in W^(1,2)(Bn, Y).
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