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A co-area formula with applications to monotone rearrangement and to regularity

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References

  1. C. Bandle, Isoperimetric Inequalities and Applications, Pitman Advanced Publishing Program, Boston, London, Melbourne, 1980.

    Google Scholar 

  2. Th. Brocker, Differential Germs and Catastrophes, Lecture Notes, Series N∘ 17. London Math. Soc.

  3. H. Federer, Geometric measure theory, Springer-Verlag, New York 1969.

    Google Scholar 

  4. H. Federer & W. Fleming, Ann. of Math. 72, 1960, pp. 458–520.

    Google Scholar 

  5. W. Fleming & E. Rischel, Arch. Math. 11, 1960, pp. 218–222.

    Google Scholar 

  6. V. Mazja, Sobolev Spaces, Springer-Verlag, 1985, Berlin Heidelberg.

    Google Scholar 

  7. C. Miranda, Partial differential equations of elliptic type, Springer-Verlag 1970, Berlin New York.

    Google Scholar 

  8. J. Mossino & R. Temam, Duke Math. J. 41, 1987, pp. 475–495.

    Google Scholar 

  9. J. Mossino & J. M. Rakotoson, Ann. Scuola Norm. Sup. Pisa, (IV)/3, 1986, pp. 51–73.

    Google Scholar 

  10. J. M. Rakotoson, Comptes Rendus Rendus Ac. Sc. Paris, 302, 1986, pp. 531–534.

    Google Scholar 

  11. J. M. Rakotoson, Réarrangement relatif dans les équations élliptiques quasilinéaires avec un second membre distribution: Application à un théorème d'existence et de régularité, Journal of Diff. Equ. 66, 1987, pp. 391–419.

    Google Scholar 

  12. J. M. Rakotoson, Existence of bounded solutions of some degenerate quasilinear elliptic problems, Comm. Part. diff. Equations 12, 1987, pp. 633–676.

    Google Scholar 

  13. J. M. Rakotoson & R. Temam, Relative rearrangement in quasilinear variational inequalities, Indiana Mathematics Journal 36, pp. 757–810. See also Compte Rendus Ac. Sc. Paris 304, 1987, pp. 527–530.

  14. J. M. Rakotoson, Réarrangement relatif: propriétés et applications aux équations aux dérivées partielles. Thése d'état, Université de Paris-Orsay. Juin 1987.

  15. J. M. Rakotoson & R. Temam, Une formule intégrale du type de Federer et Applications, Comptes Rendus Ac. Sc., Paris 304, 1987, pp. 443–446.

    Google Scholar 

  16. E. Sperner, Manusc. Math. 11, 1974, pp. 159–170.

    Google Scholar 

  17. E. C. Titchmarsch, Theory of functions 2nd ed., Oxford Univ. Press London, 1939.

    Google Scholar 

  18. E. De Giorgi, Ann. Mat. Pura ed Applicata 36, 1952, pp. 191–213.

    Google Scholar 

  19. J. M. Rakotoson, Relative Rearrangement: New results and open problems (to appear).

  20. J. M. Rakotoson, A differentiability result for the relative rearrangement, Differential and Integral Equations, to appear.

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Authors and Affiliations

  1. Institute for Applied Mathematics and Scientific Computing, Indiana University, Bloomington

    Jean Michel Rakotoson & Roger Temam

  2. Laboratoire d'Analyse Numérique, Université Paris Sud, Orsay, France

    Jean Michel Rakotoson & Roger Temam

Authors
  1. Jean Michel Rakotoson
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  2. Roger Temam
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Communicated by G. Strang

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Rakotoson, J.M., Temam, R. A co-area formula with applications to monotone rearrangement and to regularity. Arch. Rational Mech. Anal. 109, 213–238 (1990). https://doi.org/10.1007/BF00375089

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  • DOI: https://doi.org/10.1007/BF00375089

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