10 papers
A variational approach to Ornstein-Uhlenbeck evolution equations and obstacle problems
Erica Ipocoana, Annalaura Rebucci
We develop a variational formulation of the Ornstein-Uhlenbeck evolution equation based on a Gaussian divergence structure, in which the drift term is absorbed into the first varia…
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…
New perspectives on recent trends for Kolmogorov operators
Francesca Anceschi, Mirco Piccinini, Annalaura Rebucci
After carrying out an overview on the non Euclidean geometrical setting suitable for the study of Kolmogorov operators with rough coefficients, we list some properties of the funct…
On the obstacle problem associated to the Kolmogorov-Fokker-Planck operator with rough coefficients
Francesca Anceschi, Annalaura Rebucci
This work is devoted to the study of the obstacle problem associated to the Kolmogorov-Fokker-Planck operator with rough coefficients through a variational approach. In particular,…
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…
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…