Archive for Rational Mechanics and Analysis

, Volume 137, Issue 4, pp 321–340

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

  • Sergio Polidoro

DOI: 10.1007/s002050050031

Cite this article as:
Polidoro, S. Arch Rational Mech Anal (1997) 137: 321. doi:10.1007/s002050050031


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].

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