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

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

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.

Details

Language :
Italian
Database :
OpenAIRE
Journal :
Cinti, Chiara ; Nystrom, Kaj ; Polidoro, Sergio (2010) A boundary estimate for non-negative solutions to Kolmogorov operators in non-divergence form. [Preprint]
Accession number :
edsair.doi.dedup.....9ee68202614a09a8cde2588d08e1c176