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.
A boundary estimate for non-negative solutions to Kolmogorov operators in non-divergence form / C., Cinti; K., Nystrom; Polidoro, Sergio. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 191:1(2012), pp. 1-23. [10.1007/s10231-010-0172-z]
A boundary estimate for non-negative solutions to Kolmogorov operators in non-divergence form
POLIDORO, Sergio
2012
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.File | Dimensione | Formato | |
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