On a class of hypoelliptic operators with unbounded coefficients in ${\matbb R}^N$

Details On a class of hypoelliptic operators with unbounded coefficients in ${\matbb R}^N$ On a class of hypoelliptic operators with unbounded coefficients in ${\matbb R}^N$

2008-03-04

arxiv.org/abs/0803.0509v1

Mathematics

Analysis of PDEs

Scientific paper

We consider a class of non-trivial perturbations ${\mathscr A}$ of the degenerate Ornstein-Uhlenbeck operator in ${\mathbb R}^N$. In fact we perturb both the diffusion and the drift part of the operator (say $Q$ and $B$) allowing the diffusion part to be unbounded in ${\mathbb R}^N$. Assuming that the kernel of the matrix $Q(x)$ is invariant with respect to $x\in {\mathbb R}^N$ and the Kalman rank condition is satisfied at any $x\in{\mathbb R}^N$ by the same $m

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