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Integral Representation of Functionals Defined on Sobolev Spaces

  • Giovanni Alberti
  • Giuseppe Buttazzo
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 5)

Abstract

We give an integral representation result for functionals defined on Sobolev spaces; more precisely, for a functional F, we find necessary and sufficient conditions that imply the integral representation formula
$$ F(u,\,B) = \int_B {f(x,\,Du)\,dx.} $$

Keywords

Sobolev Space Integral Representation Borel Subset Borel Function Additive Functional 
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

© Birkhäuser Boston 1991

Authors and Affiliations

  • Giovanni Alberti
    • 1
  • Giuseppe Buttazzo
    • 2
  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.Dipartimento di MatematicaFerraraItaly

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