Calculus of Variations and Geometric Measure Theory

M. Giaquinta - G. Modica - D. Mucci

The relaxed Dirichlet energy of manifold constrained mappings

created by mucci on 24 Jul 2007
modified on 15 Dec 2008


Published Paper

Inserted: 24 jul 2007
Last Updated: 15 dec 2008

Journal: Advances in Calc. Var.
Volume: 1
Number: 1
Pages: 1-51
Year: 2008


The Dirichlet energy of Sobolev mappings between Riemannian manifolds is studied. After giving an explicit formula of the polyconvex extension of the energy for currents between manifolds, we prove a strong density result. As a consequence, we give an explicit formula for the relaxed energy. The fractional space of traces of $W^{1,2}$-mappings is also treated.