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Weak and strong density results for the Dirichlet energy

Mariano Giaquinta, Domenico Mucci (2004)

Journal of the European Mathematical Society

Let 𝒴 be a smooth oriented Riemannian manifold which is compact, connected, without boundary and with second homology group without torsion. In this paper we characterize the sequential weak closure of smooth graphs in B n × 𝒴 with equibounded Dirichlet energies, B n being the unit ball in n . More precisely, weak limits of graphs of smooth maps u k : B n 𝒴 with equibounded Dirichlet integral give rise to elements of the space cart 2 , 1 ( B n × 𝒴 ) (cf. [4], [5], [6]). In this paper we prove that every element T in cart 2 , 1 ( B n × 𝒴 ) is the weak limit...

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