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Annali di Matematica Pura ed Applicata

, Volume 146, Issue 1, pp 65–96 | Cite as

Compact sets in the spaceL p (O,T; B)

  • Jacques Simon
Article

Summary

A characterization of compact sets in Lp (0, T; B) is given, where 1⩽P⩾∞ and B is a Banach space. For the existence of solutions in nonlinear boundary value problems by the compactness method, the point is to obtain compactness in a space Lp (0,T; B) from estimates with values in some spaces X, Y or B where X⊂B⊂Y with compact imbedding X→B. Using the present characterization for this kind of situations, sufficient conditions for compactness are given with optimal parameters. As an example, it is proved that if {fn} is bounded in Lq(0,T; B) and in L loc 1 (0, T; X) and if {∂fn/∂t} is bounded in L loc 1 (0, T; Y) then {fn} is relatively compact in Lp(0,T; B), ∀p<q.

Keywords

Banach Space Optimal Parameter Nonlinear Boundary Compactness Method Compact Imbed 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1985

Authors and Affiliations

  • Jacques Simon
    • 1
  1. 1.Laboratoire d'Analyse Numérique(U. A. 189)Université Pierre et Marie CurieParis Cedex 05

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