| Abstract: |
| This talk presents recent results concerning global Schauder estimates for a class of kinetic-type Kolmogorov equations. We consider operators with coefficients that are H\older continuous in the space variables and merely measurable in time. After a brief overview of the existing literature and a comparison of different results, we focus on Schauder estimates expressed in terms of intrinsic H\older norms, which naturally account for the non-isotropic geometry of the underlying Lie group. We will discuss the analytical technique and outline the key steps of the proof, based on a perturbation argument and fine estimates of the fundamental solution. |
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