3 papers
math.AP2025
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…
math.AP2025
Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators
Francesca Anceschi, Helge Dietert, Jessica Guerand +5
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…
math.AP2025
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…