Schauder estimates for degenerate Levy Ornstein-Uhlenbeck operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:500

Article

Marino, Lorenzo^1,2 

[1] Univ Evry Val Essonne, Lab Modelisat Math Evry LaMME, 23 Blvd France, F-91037 Evry, France

[2] Univ Pavia, Dipartimento Matemat, Via Adolfo Ferrata 5, I-27100 Pavia, Italy

关键词: Schauder estimates;    Degenerate IPDEs;    Levy Ornstein-Uhlenbeck operators;   

DOI  :  10.1016/j.jmaa.2021.125168

来源: Elsevier

【 摘 要 】

We establish global Schauder estimates for integro-partial differential equations (IPDE) driven by a possibly degenerate Levy Ornstein-Uhlenbeck operator, both in the elliptic and parabolic setting, using some suitable anisotropic Holder spaces. The class of operators we consider is composed by a linear drift plus a Levy operator that is comparable, in a suitable sense, with a possibly truncated stable operator. It includes for example, the relativistic, the tempered, the layered or the Lamperti stable operators. Our method does not assume neither the symmetry of the Levy operator nor the invariance for dilations of the linear part of the operator. Thanks to our estimates, we prove in addition the well-posedness of the considered IPDE in suitable functional spaces. In the final section, we extend some of these results to more general operators involving non-linear, space-time dependent drifts. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free