A molecular method applied to a non-local PDE in stratified Lie groups

TL;DR

This paper investigates a transport-diffusion PDE on stratified Lie groups, establishing existence, maximum principle, positivity, and regularity results within this geometric framework.

Contribution

It introduces a molecular method tailored for non-local PDEs on stratified Lie groups, providing new analytical tools for such equations.

Findings

Proved existence of solutions

Established maximum and positivity principles

Demonstrated Hölder regularity

Abstract

In this article we study a transport-diffusion equation in the framework of the stratified Lie groups. For this equation we will study the existence of the solutions, a maximum principle, a positivity principle and H\"older regularity.