Displaying similar documents to “A-Quasiconvexity: Relaxation and Homogenization”

Integral representation and Γ-convergence of variational integrals with -growth

Alessandra Coscia, Domenico Mucci (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the integral representation properties of limits of sequences of integral functionals like   ∫ f ( x , D u ) d x   under nonstandard growth conditions of -type: namely, we assume that | z | p ( x ) ≤ f ( x , z ) ≤ L ( 1 + | z | p ( x ) ) . Under weak assumptions on the continuous function , we prove -convergence to integral functionals of the same type. We also analyse the case of integrands depending explicitly on ; finally we weaken the assumption allowing to be discontinuous on nice sets.

Lower semicontinuity of multiple µ-quasiconvex integrals

Ilaria Fragalà (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Lower semicontinuity results are obtained for multiple integrals of the kind ∫ ℝ n f ( x , ∇ μ u ) d μ , where is a given positive measure on ℝ n , and the vector-valued function belongs to the Sobolev space H μ 1 , p ( ℝ n , ℝ m ) associated with . The proofs are essentially based on blow-up techniques, and a significant role is played therein by the concepts of tangent space and of tangent measures to . More precisely, for fully general , a notion of quasiconvexity for along the tangent bundle to , turns out to be necessary for...