A boundary estimate for non-negative solutions to Kolmogorov operators in non-divergence form

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
Document type
Preprint
Creators
CreatorsAffiliationORCID
Cinti, Chiara
Nystrom, Kaj
Polidoro, Sergio
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
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