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Some variational convergence results with applications to evolution inclusions

Chapter
Part of the Advances in Mathematical Economics book series (MATHECON, volume 8)

Abstract

We study variational convergence for integral functionals defined on L H ([0, 1];dt) × y([0,1]; \( \mathbb{Y} \) ) where ℍ is a separable Hilbert space, \( \mathbb{D} \) is a Polish space and y[0,1]; \( \mathbb{D} \) ) is the space of Young measures on [0,1] × \( \mathbb{D} \) , and we investigate its applications to evolution inclusions. We prove the dependence of solutions with respect to the control Young measures and apply it to the study of the value function associated with these control problems. In this framework we then prove that the value function is a viscosity subsolution of the associated HJB equation. Some limiting properties for nonconvex integral functionals in proximal analysis are also investigated.

Key words

Young measure relaxed control semicontinuity integral functional subdifferential proximal analysis viscosity subsolution 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Département de MathématiquesUniversité Montpellier IIMontpellier Cedex 5France
  2. 2.Laboratoire Raphaël Salem, UMR CNRS 6085, UFR SciencesUniversité de RouenSaint Etienne du RouvrayFrance
  3. 3.Dipartimento di MatematicaUniversità di PerugiaPerugiaItaly

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