Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poisson process and sharp constants in Lp and Schauder estimates for a
  class of degenerate Kolmogorov operators   We consider a possibly degenerate Kolmogorov-Ornstein-Uhlenbeck operator of
the form L = Tr(BD 2) + Az, D , where A, B are N x N matrices, z $\in$ R N , N
$\ge$ 1, which satisfy the Kalman condition which is equivalent to the
hypoellipticity condition. We prove the following stability result: the
Schauder and Sobolev estimates associated with the corresponding parabolic
Cauchy problem remain valid, with the same constant, for the parabolic Cauchy
problem associated with a second order perturbation of L, namely for L +
Tr(S(t)D 2) where S(t) is a non-negative N x N matrix depending continuously on
t $\ge$ 0. Our approach relies on the perturbative technique based on the
Poisson process introduced in [15].

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The categories of this paper are: q-bio
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