Schauder estimates for degenerate stable Kolmogorov equations

Lorenzo Marino (1, 2)

1 UNIPV - Dipartimento di Matematica “Felice Casorati” Department of Mathematics [Univ Pavia]
2 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry

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 Hölder 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.

Mots clés: Schauder estimates; degenerate IPDEs; perturbation techniques; parametrix; Besov spaces

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Lorenzo Marino. Schauder estimates for degenerate stable Kolmogorov equations. 2019. ⟨hal-02305541⟩