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Displaying similar documents to “Semicontinuity of multiple integrals of the calculus of variations in parametric form”

On lower semicontinuity of multiple integrals

Agnieszka Kałamajska (1997)

Colloquium Mathematicae

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We give a new short proof of the Morrey-Acerbi-Fusco-Marcellini Theorem on lower semicontinuity of the variational functional ∫ Ω F ( x , u , ∇ u ) d x . The proofs are based on arguments from the theory of Young measures.

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...