### A Green function and regularity results for an ultraparabolic equation with a singular potential

#### Abstract

We prove a Harnack inequality for the positive solutions of a Schr\"odinger type equation $$L_0\,u\,+\,V\,u\,=\,0,$$ where $L_0$ is an operator satisfying the H\"ormander's condition and $V$ belongs to a class of functions of Stummel-Kato type. We also obtain the existence of a Green function and an uniqueness result for the Cauchy-Dirichlet problem.

#### Article information

Source
Adv. Differential Equations Volume 7, Number 11 (2002), 1281-1314.

Dates
First available in Project Euclid: 27 December 2012