About the regularity of degenerate non-local Kolmogorov operators under diffusive perturbations

We study here the effects of a time-dependent second order perturbation to a degenerate Ornstein-Uhlenbeck type operator whose diffusive part can be either local or non-local. More precisely, we establish that some estimates, such as the Schauder and Sobolev ones, already known for the non-perturbed...

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Bibliographic Details
Published in:arXiv.org 2023-06
Main Authors: Marino, Lorenzo, Menozzi, Stéphane, Priola, Enrico
Format: Article
Language:English
Subjects:
Operators
Perturbation
Time dependence
Time measurement
Online Access:Get full text
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Summary:We study here the effects of a time-dependent second order perturbation to a degenerate Ornstein-Uhlenbeck type operator whose diffusive part can be either local or non-local. More precisely, we establish that some estimates, such as the Schauder and Sobolev ones, already known for the non-perturbed operator still hold, and with the same constants, when we perturb the Ornstein-Uhlenbeck operator with second order diffusions with coefficients only depending on time in a measurable way. The aim of the current work is twofold: we weaken the assumptions required on the perturbation in the local case which has been considered already in [KP17] and we extend the approach presented therein to a wider class of degenerate Kolmogorov operators with non-local diffusive part of symmetric stable type.
ISSN:2331-8422