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Density results relative to the Dirichlet energy of mappings into a manifold
Author(s) -
Giaquinta Mariano,
Mucci Domenico
Publication year - 2006
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20125
Subject(s) - mathematics , riemannian manifold , dirichlet distribution , torsion (gastropod) , pure mathematics , manifold (fluid mechanics) , mathematical analysis , dirichlet's energy , dirichlet integral , dirichlet problem , dimension (graph theory) , combinatorics , boundary value problem , medicine , mechanical engineering , surgery , engineering
Let be a smooth, compact, oriented Riemannian manifold without boundary. Weak limits of graphs of smooth maps u k : B n → with an equibounded Dirichlet integral give rise to elements of the space cart 2,1 ( B n × ). Assume that 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 × ) 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 → with Dirichlet energies converging to the energy of T . © 2006 Wiley Periodicals, Inc.