# 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]
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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
Document type
Preprint
Creators
CreatorsAffiliationORCID
Cinti, Chiara
Polidoro, Sergio
Keywords
Cauchy problem, Kolmogorov operator, hypoelliptic PDEs, Lie groups
Subjects
DOI
Deposit date
21 Jan 2008