6 papers
Harnack inequality and asymptotic lower bounds for the relativistic Fokker-Planck operator
Francesca Anceschi, Sergio Polidoro, Annalaura Rebucci
We consider a class of second order degenerate kinetic operators in the framework of special relativity. We first describe as an Hörmander operator whic…
A Yosida's parametrix approach to Varadhan's estimates for a degenerate diffusion under the weak Hörmander condition
Stefano Pagliarani, Sergio Polidoro
We adapt and extend Yosida's parametrix method, originally introduced for the construction of the fundamental solution to a parabolic operator on a Riemannian manifold, to derive V…
Schauder type estimates for degenerate Kolmogorov equations with Dini continuous coefficients
Sergio Polidoro, Annalaura Rebucci, Bianca Stroffolini
We study the regularity properties of the second order linear operator in : \begin{equation*} \mathscr{L} u := \sum_{j,k= 1}^{m} a_{jk}\partial_{x_j x_k}^2 u + \s…
Fundamental solutions for Kolmogorov-Fokker-Planck operators with time-depending measurable coefficients
Marco Bramanti, Sergio Polidoro
We consider a Kolmogorov-Fokker-Planck operator of the kind studied by Lanconelli-Polidoro in [Rend. Sem. Mat. Univ. Politec. Torino 52 (1994)], where the leading coefficients $a_{…
A survey on the classical theory for Kolmogorov equation
Francesca Anceschi, Sergio Polidoro
We present a survey on the regularity theory for classic solutions to subelliptic degenerate Kolmogorov equations. In the last part of this note we present a detailed proof of a Ha…
Moser's estimates for degenerate Kolmogorov equations with non-negative divergence lower order coefficients
Francesca Anceschi, Sergio Polidoro, Maria Alessandra Ragusa
We prove the local boundedness of the solutions to degenerate second order partial differential equations of Kolmogorov type with measurable coefficients in divergence form, under…