Calculus of Variations and Geometric Measure Theory

M. Giaquinta - D. Mucci

The relaxed Dirichlet energy of mappings into a manifold

created by mucci on 09 Nov 2004
modified on 21 Nov 2005


Published Paper

Inserted: 9 nov 2004
Last Updated: 21 nov 2005

Journal: Calc. Var.
Volume: 24
Number: 2
Pages: 155-166
Year: 2005

DOI: 10.1007s00526-004-0318-1


Let \,${\cal Y}$\, be a smooth 1-connected compact oriented manifold without boundary, such that its $2$-homology group has no torsion. We characterize in any dimension \,$n$\, the weak \,$W^{1,2}(B^n,{\cal Y})$ lower semicontinuous envelope of the Dirichlet integral of Sobolev maps in \,$W^{1,2}(B^n,{\cal Y})$.