Cinti, Chiara ; Nystrom, Kaj ; Polidoro, Sergio
(2010)
*A boundary estimate for non-negative solutions to Kolmogorov operators in non-divergence form.*
[Preprint]

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## Abstract

We consider non-negative solutions to a class of second order degenerate Kolmogorov operators L in non-divergence form, defined in a bounded open domain Omega contained in R^{N+1}. Let K be a compact subset of the closure of Omega, let z be a point of Omega, and let Sigma be a subset of the boundary of Omega. We give sufficient geometric conditions for the validity of the following Carleson type estimate: There exists a positive constant C, depending only on the Kolmogorov operator L, on Omega, Sigma, K and z, such that
sup_K u < C u(z),
for every non-negative solution u of Lu = 0 in Omega such that u vanishes on Sigma.

Abstract

We consider non-negative solutions to a class of second order degenerate Kolmogorov operators L in non-divergence form, defined in a bounded open domain Omega contained in R^{N+1}. Let K be a compact subset of the closure of Omega, let z be a point of Omega, and let Sigma be a subset of the boundary of Omega. We give sufficient geometric conditions for the validity of the following Carleson type estimate: There exists a positive constant C, depending only on the Kolmogorov operator L, on Omega, Sigma, K and z, such that
sup_K u < C u(z),
for every non-negative solution u of Lu = 0 in Omega such that u vanishes on Sigma.

Document type

Preprint

Creators

Keywords

Kolmogorov equations, Hormander condition, Harnack inequality,
boundary behavior, Carleson type inequality

Subjects

DOI

Deposit date

13 Jul 2010 09:24

Last modified

17 Feb 2016 15:09

URI

## Other metadata

Document type

Preprint

Creators

Keywords

Kolmogorov equations, Hormander condition, Harnack inequality,
boundary behavior, Carleson type inequality

Subjects

DOI

Deposit date

13 Jul 2010 09:24

Last modified

17 Feb 2016 15:09

URI

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