Integral Representation of Abstract Functionals of Autonomous Type
نویسنده
چکیده
In this work we extend the results of [2] to a family of abstract functionals of autonomous type satisfying suitable locality and additivity properties, and general integral growth conditions of superlinear type. We single out a condition which is necessary and sufficient in order for a functional of this class to admit an integral representation, and sufficient as well to have an integral representation for its lower semicontinuous envelope. We also show that the integrand F (x, q) satisfies some nice regularity properties in the q–variable, in particular a convexity–type property along lines. By adapting to the case at issue the reparametrization techniques introduced in [17], we then prove that the family of integral functionals associated to integrands of this kind do meet the condition mentioned above, in particular it is closed by Γ–convergence.
منابع مشابه
A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces
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