Displaying similar documents to “Cartesian currents in the calculus of variations”

Some remarks about the p -Dirichlet integral

Mariano Giaquinta, Giuseppe Modica, Jiří Souček (1994)

Commentationes Mathematicae Universitatis Carolinae

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We discuss variational problems for the p -Dirichlet integral, p non integer, for maps between manifolds, illustrating the role played by the geometry of the target manifold in their weak formulation.

The BV-energy of maps into a manifold : relaxation and density results

Mariano Giaquinta, Domenico Mucci (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let  𝒴   be a smooth compact oriented riemannian manifoldwithout boundary, and assume that its 1 -homology group has notorsion. Weak limits of graphs of smooth maps  u k : B n → 𝒴   with equibounded total variation give riseto equivalence classes of cartesian currents in  cart 1 , 1 ( B n 𝒴 )   for which we introduce a natural B V -energy.Assume moreover that the first homotopy group of   𝒴   iscommutative. In any dimension   n   we prove that every element  T   in   cart 1 , 1 ( B n 𝒴 )   can be approximatedweakly in the sense of currents by a sequence...