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

Authors: Nicola Garofalo and Ermanno Lanconelli
Journal: Trans. Amer. Math. Soc. 321 (1990), 775-792
MSC: Primary 35K65; Secondary 35A30, 35B05
MathSciNet review: 998126
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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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