Archive for Rational Mechanics and Analysis

, Volume 137, Issue 4, pp 321–340 | Cite as

A Global Lower Bound for the Fundamental Solution of Kolmogorov-Fokker-Planck Equations

  • Sergio Polidoro

Abstract

The main result of this paper is a global lower bound for the fundamental solution Γ of the ultraparabolic differential operator
$$$$

where the ai, j's and their first derivatives are Hölder continuous functions and 0 < p0 < N. The bound will follow from a local estimate of Γ and a Harnack inequality for non-negative solutions of Lu = 0, by exploiting the invariance of the Harnack inequality with respect to suitable translation and dilation groups. For non-degenerate parabolic operators, our methods and results generalize those of Aronson & Serrin [1].

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Sergio Polidoro
    • 1
  1. 1.Dipartimento di Matematica Piazza di Porta S. Donato, 5 40127, Bologna, ItalyIT

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