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The Space SBV(Ω) and Free Discontinuity Problems

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Variational and Free Boundary Problems

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 53))

Abstract

This paper deals with variational problems which have among the unknowns an hypersurface. In order to deal with these problems, it has been introduced in [15] the space SBV(Ω) of “special” functions with bounded variation. By summarizing the results of [2] and [4], we recall here the definition and the main compactness properties of SBV(Ω). In addition, we state lower semicontinuity criteria for integral functionals defined in SBV(Ω). Finally, we show how these variational problems can be approximated by others, more tractable from the numerical point of view.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, II Università di Roma, Tor Vergata, Roma, Italy

    Luigi Ambrosio

Authors
  1. Luigi Ambrosio
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Editor information

Editors and Affiliations

  1. Institute for Mathematics and its Applications, University of Minnesota, 55455, Minneapolis, MN, USA

    Avner Friedman

  2. Department of Mathematics, Johns Hopkins University, 21218, Baltimore, MD, USA

    Joel Spruck

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© 1993 Springer-Verlag New York, Inc.

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Ambrosio, L. (1993). The Space SBV(Ω) and Free Discontinuity Problems. In: Friedman, A., Spruck, J. (eds) Variational and Free Boundary Problems. The IMA Volumes in Mathematics and its Applications, vol 53. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8357-4_3

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  • DOI: https://doi.org/10.1007/978-1-4613-8357-4_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8359-8

  • Online ISBN: 978-1-4613-8357-4

  • eBook Packages: Springer Book Archive

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