Bounds on short cylinders and uniqueness results for degenerate Kolmogorov equation

Cinti, Chiara ; Polidoro, Sergio (2008) Bounds on short cylinders and uniqueness results for degenerate Kolmogorov equation. [Preprint]
Full text available as:
[thumbnail of Paper.pdf]
Download (228kB) | Preview


We consider the Cauchy problem for hypoelliptic Kolmogorov equations in both divergence and non divergence form. We prove that, if |u(x,t)| < M exp(a(t^{-\beta}+|x|^2)) for some positive constants a, M, \beta in ]0,1[ and u(x,0) = 0, then u(x,t) = 0 for positive t. The proof of the main result is based on some previous uniqueness result and on the application of some estimates in short cylinders, first introduced by Safonov in the study of uniformly parabolic operators.

Document type
Cinti, Chiara
Polidoro, Sergio
Cauchy problem, Kolmogorov operator, hypoelliptic PDEs, Lie groups
Deposit date
21 Jan 2008
Last modified
16 May 2011 12:07

Other metadata

This work may be freely consulted and used, may be reproduced on a permanent basis in a digital format (i.e. saving) and can be printed on paper with own personal equipment (without availing of third -parties services), for strictly and exclusively personal, research or teaching purposes, with express exclusion of any direct or indirect commercial use, unless otherwise expressly agreed between the user and the author or the right holder. It is also allowed, for the same purposes mentioned above, the retransmission via telecommunication network, the distribution or sending in any form of the work, including the personal redirection (e-mail), provided it is always clearly indicated the complete link to the page of the Alma DL Site in which the work is displayed. All other rights are reserved.



Staff only: View the document