Let Y be a smooth, compact, oriented Riemannian manifold without boundary. Weak limits of graphs of smooth maps uk : Bn → Y with an equibounded Dirichlet integral give rise to elements of the space cart2,1(Bn × 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 cart2,1(Bn ×Y) with no singular vertical part can be approximated weakly in the sense of currents by a sequence of graphs of smooth maps uk : Bn → Y with Dirichlet energies converging to the energy of T .

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

GIAQUINTA, Mariano;
2006

Abstract

Let Y be a smooth, compact, oriented Riemannian manifold without boundary. Weak limits of graphs of smooth maps uk : Bn → Y with an equibounded Dirichlet integral give rise to elements of the space cart2,1(Bn × 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 cart2,1(Bn ×Y) with no singular vertical part can be approximated weakly in the sense of currents by a sequence of graphs of smooth maps uk : Bn → Y with Dirichlet energies converging to the energy of T .
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/6542
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