Annali di Matematica Pura ed Applicata

, Volume 110, Issue 1, pp 353–372 | Cite as

Best constant in Sobolev inequality

  • Giorgio Talenti
Article

Summary

The best constant for the simplest Sobolev inequality is exhibited. The proof is accomplished by symmetrizations (rearrangements in the sense of Hardy-Littlewood) and one-dimensional calculus of variations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    L. Bers - F. John - M. Schechter,Partial Differential Equations, Interscience (1964)Google Scholar
  2. [2]
    G. A. Bliss,An integral inequality, Journal London Math. Soc.,5 (1930).Google Scholar
  3. [3]
    H. Federer,Curvature measure, Trans. Amer. Math. Soc.,93 (1959).Google Scholar
  4. [4]
    H. Federer - W. Fleming,Normal and integral currents, Annals of Math.,72 (1960).Google Scholar
  5. [5]
    W. Fleming,Functions whose partial derivatives are measures, Illinois J. Math.,4 (1960).Google Scholar
  6. [6]
    W. Fleming - R. Rishel,An integral formula for total gradient variation, Arch. Math.,11 (1960).Google Scholar
  7. [7]
    M. Miranda,Distribuzioni aventi derivate misure, Ann. Scuola Norm. Sup. Pisa,18 (1964).Google Scholar
  8. [8]
    M. Miranda,Sul minimo dell'integrale del gradiente di una funzione, Ann. Scuola Norm. Sup. Pisa,19 (1965).Google Scholar
  9. [9]
    M. Miranda,Disuguaglianze di Sobolev sulle ipersuperfici minimali, Rend. Sem. Mat. Univ. Padova,38 (1967).Google Scholar
  10. [10]
    G. Rosen,Minimum value for c in the Sobolev inequality, SIAM J. Appl. Math.,21 (1971).Google Scholar
  11. [11]
    S. L. Sobolev,On a theorem of functional analysis (in russian), Mat. Sb.,4 (1938).Google Scholar
  12. [12]
    S. L. Sobolev,Applications of functional analysis in mathematical physics, Amer. Math. Soc. (1963).Google Scholar
  13. [13]
    L. C. Young,Partial area, Rivista Mat. Univ. Parma,10 (1959).Google Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1975

Authors and Affiliations

  • Giorgio Talenti
    • 1
  1. 1.Firenze

Personalised recommendations