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Article Dans Une Revue International Mathematics Research Notices Année : 2013

The Harnack inequality for a class of degenerate elliptic operators

Andrej Zlatos
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Résumé

We prove a Harnack inequality for distributional solutions to a type of degenerate elliptic PDEs in $N$ dimensions. The differential operators in question are related to the Kolmogorov operator, made up of the Laplacian in the last $N-1$ variables, a first-order term corresponding to a shear flow in the direction of the first variable, and a bounded measurable potential term. The first-order coefficient is a smooth function of the last $N-1$ variables and its derivatives up to certain order do not vanish simultaneously at any point, making the operators in question hypoelliptic.
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Dates et versions

hal-00651853 , version 1 (14-12-2011)

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Francois Hamel, Andrej Zlatos. The Harnack inequality for a class of degenerate elliptic operators. International Mathematics Research Notices, 2013, pp.10.1093/imrn/rns157. ⟨10.1093/imrn/rns157⟩. ⟨hal-00651853⟩
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