Potential Analysis

, Volume 4, Issue 4, pp 429–467

Parabolic Harnack inequality for divergence form second order differential operators

  • L. Saloff-Coste

DOI: 10.1007/BF01053457

Cite this article as:
Saloff-Coste, L. Potential Anal (1995) 4: 429. doi:10.1007/BF01053457


Old and recent results concerning Harnack inequalities for divergence form operators are reviewed. In particular, the characterization of the parabolic Harnack principle by simple geometric properties -Poincaré inequality and doubling property- is discussed at length. It is shown that these two properties suffice to apply Moser's iterative technique.

Key words

Harnack inequalityPoincaré inequalitydoubling propertyheat equation

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • L. Saloff-Coste
    • 1
  1. 1.CNRS, Statistique et ProbabilitésUniversité SabatierToulouse cedexFrance