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European Congress of Mathematics pp 317–326Cite as

Birkhäuser

The Calibration Method for Free Discontinuity Problems

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Part of the book series: Progress in Mathematics ((PM,volume 201))

Abstract

The calibration method is used to identify some minimizers of the Mumford-Shah functional. The method is then extended to more general free discontinuity problems.

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References

  1. G. Alberti, G. Bouchitté and G. Dal Maso: The calibration method for the Mumford Shah functional and free discontinuity problems,Preprint SISSA, Trieste, 2001.

    Google Scholar 

  2. L. Ambrosio, N. Fusco and D. Pallara: Functions of Bounded Variation and Free Discontinuity Problems, Oxford Mathematical Monographs, Oxford University Press, Oxford, 2000.

    MATH  Google Scholar 

  3. A. Chambolle: Personal communication, Trieste, 1996.

    Google Scholar 

  4. G. Dal Maso, M.G. Mora and M. Morini: Local calibration for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets, J. Math. Pures Appl., 79 (2000), 141–162.

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  5. E. De Giorgi: Free discontinuity problems in calculus of variations, in: Frontiers in Pure and Applied Mathemathics, a collection of papers dedicated to Jacques-Louis Lions on the occasion of his sixtieth birthday, R. Dautray ed., North Holland, Amsterdam (1991), 55–62.

    Google Scholar 

  6. E. De Giorgi and L. Ambrosio: Un nuovo funzionale del calcolo delle variazioni,Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 82 (1988), 199–210.

    MathSciNet  MATH  Google Scholar 

  7. H. Federer: Geometric Measure Theory, Springer-Verlag, Berlin, 1969.

    MATH  Google Scholar 

  8. M. G. Mora and M. Morini: Local calibration for minimizers of the Mumford-Shah functional with a regular discontinuity sets, Ann. Inst. H. Poincaré, Anal. Non Linéaire, to appear.

    Google Scholar 

  9. J.-M. Morel and S. Solimini: Variational Methods in Image Segmentation, Progr. Nonlinear Differential Equations Appl., 14 (1995), Birkhäuser, Boston.

    Book  Google Scholar 

  10. D. Mumford and J. Shah: Optimal approximation by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math., 42 (1989), 577–685.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. SISSA, Via Beirut 4, 34014, Trieste, Italy

    Gianni Dal Maso

Authors
  1. Gianni Dal Maso
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Editor information

Editors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    Carles Casacuberta  & Joan Verdera  & 

  2. Departament d’Algebra i Geometria Facultat de Matemàtiques, Universitat de Barcelona, 08007, Barcelona, Spain

    Rosa Maria Miró-Roig

  3. Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, 08028, Barcelona, Spain

    Sebastià Xambó-Descamps

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© 2001 Springer Basel AG

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Dal Maso, G. (2001). The Calibration Method for Free Discontinuity Problems. In: Casacuberta, C., Miró-Roig, R.M., Verdera, J., Xambó-Descamps, S. (eds) European Congress of Mathematics. Progress in Mathematics, vol 201. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8268-2_18

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  • DOI: https://doi.org/10.1007/978-3-0348-8268-2_18

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9497-5

  • Online ISBN: 978-3-0348-8268-2

  • eBook Packages: Springer Book Archive

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