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Parabolic Harnack inequality for divergence form second order differential operators

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Potential Theory and Degenerate Partial Differential Operators

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Abstract

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.

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Authors and Affiliations

  1. CNRS, Statistique et Probabilités, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse cedex, France

    L. Saloff-Coste

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  1. Department of Mathematics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy

    Marco Biroli

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Saloff-Coste, L. (1995). Parabolic Harnack inequality for divergence form second order differential operators. In: Biroli, M. (eds) Potential Theory and Degenerate Partial Differential Operators. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0085-4_9

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  • DOI: https://doi.org/10.1007/978-94-011-0085-4_9

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  • Print ISBN: 978-94-010-4042-6

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