Archive for Rational Mechanics and Analysis

, Volume 96, Issue 4, pp 327–338

A new proof of Moser's parabolic harnack inequality using the old ideas of Nash

  • E. B. Fabes
  • D. W. Stroock
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. G. Aronson, Bounds for the fundamental solution of a parabolic equation, Bulletin of the American Mathematical Society 73 (1967), 890–896.Google Scholar
  2. 2.
    D. G. Aronson & J. Serrin, Local behavior of solutions of quasilinear parabolic equations, Arch. Rational Mech. Anal. 25 (1967), 81–122.Google Scholar
  3. 3.
    E. B. Davies, Explicit constants for Gaussian upper bounds on heat kernels, to appear.Google Scholar
  4. 4.
    E. De Giorgi, Sulle differentiabilità e l'analiticità degli integrali multipli regolari, Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. (III) (1957), 25–43.Google Scholar
  5. 5.
    S. Kusuoka & D. W. Stroock, Applications of the Malliavin Calculus, Part III, to appear.Google Scholar
  6. 6.
    J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), 47–79.Google Scholar
  7. 7.
    J. Moser, A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math. 17 (1964), 101–134; Correction to “A Harnack inequality for parabolic differential equations”, Comm. Pure Appl. Math. 20 (1960), 232–236.Google Scholar
  8. 8.
    J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. math. 80 (1958), 931–954.Google Scholar
  9. 9.
    M. N. Safanov, Harnack's inequality for elliptic equations and the Hölder property of their solutions, J. Soviet Mathematics 21 (1983), 851–863.Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • E. B. Fabes
    • 1
    • 2
  • D. W. Stroock
    • 1
    • 2
  1. 1.School of Mathematics University of Minnesota
  2. 2.Department of MathematicsMassachusetts Institute of Technology

Personalised recommendations