Schauder estimates for degenerate stable Kolmogorov equations

We provide here global Schauder-type estimates for a chain of integro-partial differential equations (IPDE) driven by a degenerate stable Ornstein-Uhlenbeck operator possibly perturbed by a deterministic drift, when the coefficients lie in some suitable anisotropic H{\"o}lder spaces. Our approa...

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Bibliographic Details
Published in:arXiv.org 2019-10
Main Author: Marino, Lorenzo
Format: Article
Language:English
Subjects:
Estimates
Function space
Mathematical analysis
Partial differential equations
Well posed problems
Online Access:Get full text
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Summary:We provide here global Schauder-type estimates for a chain of integro-partial differential equations (IPDE) driven by a degenerate stable Ornstein-Uhlenbeck operator possibly perturbed by a deterministic drift, when the coefficients lie in some suitable anisotropic H{\"o}lder spaces. Our approach mainly relies on a perturbative method based on forward parametrix expansions and, due to the low regularizing properties on the degenerate variables and to some integrability constraints linked to the stability index, it also exploits duality results between appropriate Besov Spaces. In particular, our method also applies in some super-critical cases. Thanks to these estimates, we show in addition the well-posedness of the considered IPDE in a suitable functional space.
ISSN:2331-8422