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Article Dans Une Revue Studia Mathematica Année : 2022

Poisson process and sharp constants in Lp and Schauder estimates for a class of degenerate Kolmogorov operators

Résumé

We consider a possibly degenerate Kolmogorov-Ornstein-Uhlenbeck operator of the form L = Tr(BD 2) + Az, D , where A, B are N × N matrices, z ∈ R N , N ≥ 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 × N matrix depending continuously on t ≥ 0. Our approach relies on the perturbative technique based on the Poisson process introduced in [15].
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Dates et versions

hal-03284221 , version 1 (13-07-2021)
hal-03284221 , version 2 (30-08-2021)
hal-03284221 , version 3 (26-09-2021)

Identifiants

Citer

L. Marino, S. Menozzi, E. Priola. Poisson process and sharp constants in Lp and Schauder estimates for a class of degenerate Kolmogorov operators. Studia Mathematica, 2022, 267 (3), pp.321-346. ⟨10.4064/sm210819-13-4⟩. ⟨hal-03284221v3⟩
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