Level sets of the fundamental solution and Harnack inequality for degenerate equations of Kolmogorov type

Garofalo, Nicola; Lanconelli, Ermanno

doi:10.1090/S0002-9947-1990-0998126-5

Level sets of the fundamental solution and Harnack inequality for degenerate equations of Kolmogorov type
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by Nicola Garofalo and Ermanno Lanconelli PDF

Trans. Amer. Math. Soc. 321 (1990), 775-792 Request permission

Abstract:

In this paper we establish a uniform Harnack inequality for a class of degenerate equations whose prototype is Kolmogorov’s equations in ${{\mathbf {R}}^3}:{D_{{\text {yy}}}}u - {\text {y}}{D_z}u - {D_t}u = 0$. Our approach is based on mean value formulas for solutions of the equation under consideration on the level sets of the fundamental solution.

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