Parabolic Harnack inequality for divergence form second order differential operators



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 inequality Poincaré inequality doubling property heat equation 


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© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  1. 1.CNRS, Statistique et ProbabilitésUniversité Paul SabatierToulouse cedexFrance

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