We consider weak solutions of second-order partial differential equations of Kolmogorov-Fokker-Planck-type with measurable coefficients in the form ∂tu + (v,∇xu) = div(A(v,x,t)∇vu) + (b(v,x,t),∇vu) + f, (v,x,t) ϵ2n+1, where A is a symmetric uniformly positive definite matrix with bounded measurable coefficients; f and the components of the vector b are bounded and measurable functions. We give a geometric statement of the Harnack inequality recently proved by Golse et al. As a corollary, we obtain a strong maximum principle.

A geometric statement of the Harnack inequality for a degenerate Kolmogorov equation with rough coefficients / Anceschi, Francesca; Eleuteri, Michela; Polidoro, Sergio. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 21:7(2019), pp. 1-17. [10.1142/S0219199718500578]

A geometric statement of the Harnack inequality for a degenerate Kolmogorov equation with rough coefficients

ANCESCHI, FRANCESCA;Michela Eleuteri
;
Sergio Polidoro
2019

Abstract

We consider weak solutions of second-order partial differential equations of Kolmogorov-Fokker-Planck-type with measurable coefficients in the form ∂tu + (v,∇xu) = div(A(v,x,t)∇vu) + (b(v,x,t),∇vu) + f, (v,x,t) ϵ2n+1, where A is a symmetric uniformly positive definite matrix with bounded measurable coefficients; f and the components of the vector b are bounded and measurable functions. We give a geometric statement of the Harnack inequality recently proved by Golse et al. As a corollary, we obtain a strong maximum principle.
13-set-2018
21
7
1
17
A geometric statement of the Harnack inequality for a degenerate Kolmogorov equation with rough coefficients / Anceschi, Francesca; Eleuteri, Michela; Polidoro, Sergio. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 21:7(2019), pp. 1-17. [10.1142/S0219199718500578]
Anceschi, Francesca; Eleuteri, Michela; Polidoro, Sergio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1166836
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