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Annali di Matematica Pura ed Applicata

, Volume 139, Issue 1, pp 191–225 | Cite as

Rappresentazione con integrali multipli di funzionali dipendenti da funzioni a valori in uno spazio di Banach

  • Gianfranco Bottaro
  • Pirro Oppezzi
Article

Summary

We consider a functional J: W 10c 1,p (Ω, X) ×B(Ω) → [0, ∞], where X is a Banach space andB(Ω) the class of the Borel subsets of the open Ω ⊂ Rn, and we assume that J has a suitable semicontinuity property respect its first variable, and depends like a measure from the elements ofB(Ω). We show that under certain conditions such a functional can be represented like a multiple integral of a Caratheodory integrand. The first paragraph is devoted to improve some classical results about Sobolev spaces W1,p(Ω, R) in the case of W1,p(Ω, X).

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1985

Authors and Affiliations

  • Gianfranco Bottaro
  • Pirro Oppezzi
    • 1
  1. 1.Genova

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