Cinti, Chiara ; Polidoro, Sergio
(2008)
Bounds on short cylinders and uniqueness results for degenerate Kolmogorov equation.
[Preprint]
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Abstract
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.
Abstract
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
Preprint
Creators
Keywords
Cauchy problem, Kolmogorov operator, hypoelliptic PDEs, Lie groups
Subjects
DOI
Deposit date
21 Jan 2008
Last modified
16 May 2011 12:07
URI
Other metadata
Document type
Preprint
Creators
Keywords
Cauchy problem, Kolmogorov operator, hypoelliptic PDEs, Lie groups
Subjects
DOI
Deposit date
21 Jan 2008
Last modified
16 May 2011 12:07
URI
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