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)


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
$$ F(u,\,B) = \int_B {f(x,\,Du)\,dx.} $$


Sobolev Space Integral Representation Borel Subset Borel Function Additive Functional 


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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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