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 .File in questo prodotto:
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