7 papers
Fundamental solution and Harnack inequality for subelliptic evolution operators on Carnot groups
Giulio Pecorella, Annalaura Rebucci
In this paper we study regularity properties of a class of subelliptic evolution operators. We first prove the existence of the fundamental solution by means of Levi's parametrix m…
Geometric interpretation of the vanishing Lie Bracket for two-dimensional rough vector fields
Annalaura Rebucci, Martina Zizza
In this paper, we prove that if are continuous, Sobolev vector fields with bounded divergence on the real plane and , then their flows commute. In particular, we imp…
Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators
Francesca Anceschi, Helge Dietert, Jessica Guerand +3
We propose a systematic approach based on trajectories to prove a Poincaré inequality for weak non-negative sub-solutions to hypoelliptic equations with an arbitrary number of Hörm…
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 note on the weak regularity theory for degenerate Kolmogorov equations
Francesca Anceschi, Annalaura Rebucci
The aim of this work is to prove a Harnack inequality and the Hölder continuity for weak solutions to the Kolmogorov equation with measurable coefficients, inte…
Pointwise estimates for degenerate Kolmogorov equations with -source term
Erica Ipocoana, Annalaura Rebucci
The aim of this paper is to establish new pointwise regularity results for solutions to degenerate second order partial differential equations with a Kolmogorov-type operator of th…