# Spatial regularity for a class of degenerate Kolmogorov equations

@inproceedings{Anceschi2021SpatialRF, title={Spatial regularity for a class of degenerate Kolmogorov equations}, author={Francesca Anceschi}, year={2021} }

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, i.e. x1, . . . , xm0 . 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…

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