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A boundary estimate for non-negative solutions to Kolmogorov operators in non-divergence form
- 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.
- Subjects :
- Matematik
Applied Mathematics
Mathematical analysis
Degenerate energy levels
Boundary (topology)
Sigma
MAT/05 Analisi matematica
Divergence
Kolmogorov equations
Hormander condition
Harnack inequality
boundary behavior
Carleson type inequality
Kolmogorov equations (Markov jump process)
Partial derivative
Mathematics
Mathematical physics
Harnack's inequality
Subjects
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