Spatial regularity for a class of degenerate Kolmogorov equations

2021/10/13 by Francesca Anceschi, Anceschi, Francesca
Mathematics · #35B45 #35K70 #35Q84 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2110.06585

openalex publication_date 2021/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish spatial a priori estimates for the solution u to a class of dilation invariant Kolmogorov equation, where u is assumed to only have a certain amount of regularity in the diffusion's directions. The result is that u is also regular with respect to the remaining directions. The approach we propose is based on the commutators identities and allows us to obtain a Sobolev exponent that does not depend on the integrability assumption of the right-hand side. Lastly, we provide an alternative proof to that of Theorem 1.5 of [9] for the optimal spatial regularity.

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