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Advances in Mathematical Economics pp 33–73Cite as

Some variational convergence results with applications to evolution inclusions

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Part of the book series: Advances in Mathematical Economics ((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.

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Author information

Authors and Affiliations

  1. Département de Mathématiques, Université Montpellier II, 34095, Montpellier Cedex 5, France

    Charles Castaing

  2. Laboratoire Raphaël Salem, UMR CNRS 6085, UFR Sciences, Université de Rouen, Avenue de l’Université, BP.12, 76801, Saint Etienne du Rouvray, France

    Paul Raynaud de Fitte

  3. Dipartimento di Matematica, Università di Perugia, via Vanvitelli 1, 06123, Perugia, Italy

    Anna Salvadori

Authors
  1. Charles Castaing
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  2. Paul Raynaud de Fitte
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  3. Anna Salvadori
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Editor information

Editors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-0041, Japan

    Shigeo Kusuoka (Professor) (Professor)

  2. Graduate Faculty of Economics, Hitotsubashi University, Kunitachi, Tokyo, 186-8601, Japan

    Akira Yamazaki (Professor) (Professor)

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© 2006 Springer-Verlag

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Castaing, C., de Fitte, P.R., Salvadori, A. (2006). Some variational convergence results with applications to evolution inclusions. In: Kusuoka, S., Yamazaki, A. (eds) Advances in Mathematical Economics. Advances in Mathematical Economics, vol 8. Springer, Tokyo. https://doi.org/10.1007/4-431-30899-7_2

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