The heat equation with singular potentials. II: Hypoelliptic case

Abstract

In this paper we consider the heat equation with a strongly singular potential and show that it has a very weak solution. Our analysis is devoted to general hypoelliptic operators and is developed in the setting of graded Lie groups. The current work continues and extends a previous work , where the classical heat equation on ${\mathbb{R}}^n$ was considered.

This work is a continuation of the work arXiv:2004.11255v3. It is 21 pages