Let Y be a smooth compact oriented Riemannian manifold without boundary. Weak limits of graphs of smooth maps u_k:B^n\to Y with equibounded Dirichlet integral give rise to elements of the space cart^{2,1}(B^n\times Y). Assume that Y is 1-connected and that its 2-homology group has no torsion. In any dimension n we prove that every element T in cart^{2,1}(B^n\times Y) with no singular vertical part can be approximated weakly in the sense of currents by a sequence of graphs of smooth maps u_k:B^n\to Y with Dirichlet energies converging to the energy of T.

Density results relative to the Dirichlet energy of mappings into a manifold / Giaquinta, M; Mucci, Domenico. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - 59:12(2006), pp. 1791-1810. [10.1002/cpa.20125]

### Density results relative to the Dirichlet energy of mappings into a manifold

#### Abstract

Let Y be a smooth compact oriented Riemannian manifold without boundary. Weak limits of graphs of smooth maps u_k:B^n\to Y with equibounded Dirichlet integral give rise to elements of the space cart^{2,1}(B^n\times Y). Assume that Y is 1-connected and that its 2-homology group has no torsion. In any dimension n we prove that every element T in cart^{2,1}(B^n\times Y) with no singular vertical part can be approximated weakly in the sense of currents by a sequence of graphs of smooth maps u_k:B^n\to Y with Dirichlet energies converging to the energy of T.
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Density results relative to the Dirichlet energy of mappings into a manifold / Giaquinta, M; Mucci, Domenico. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - 59:12(2006), pp. 1791-1810. [10.1002/cpa.20125]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/1511079
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