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Displaying similar documents to “On measure differential inclusions in optimal control theory.”

Lower semicontinuity of multiple μ -quasiconvex integrals

Ilaria Fragalà (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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Lower semicontinuity results are obtained for multiple integrals of the kind n f ( x , μ u ) d μ , where μ is a given positive measure on n , and the vector-valued function u belongs to the Sobolev space H μ 1 , p ( n , m ) associated with μ . 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 μ . More precisely, for fully general μ , a notion of quasiconvexity for f along the tangent bundle to μ , turns out to be necessary...