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Integral Representation of Functionals Defined on Sobolev Spaces

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Composite Media and Homogenization Theory

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((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

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

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Author information

Authors and Affiliations

  1. Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126, Pisa, Italy

    Giovanni Alberti

  2. Dipartimento di Matematica, Via Machiavelli, 35, 44100, Ferrara, Italy

    Giuseppe Buttazzo

Authors
  1. Giovanni Alberti
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  2. Giuseppe Buttazzo
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Editor information

Editors and Affiliations

  1. Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy

    Gianni Dal Maso

  2. Dipartimento di Matematica, Università “La Sapienza”, Roma, Italy

    Gian Fausto Dell’Antonio

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© 1991 Birkhäuser Boston

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Alberti, G., Buttazzo, G. (1991). Integral Representation of Functionals Defined on Sobolev Spaces. In: Dal Maso, G., Dell’Antonio, G.F. (eds) Composite Media and Homogenization Theory. Progress in Nonlinear Differential Equations and Their Applications, vol 5. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6787-1_1

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  • DOI: https://doi.org/10.1007/978-1-4684-6787-1_1

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4684-6789-5

  • Online ISBN: 978-1-4684-6787-1

  • eBook Packages: Springer Book Archive

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