Revista Matemática Iberoamericana


Full-Text PDF (307 KB) | Metadata | Table of Contents | RMI summary
Volume 24, Issue 3, 2008, pp. 1011–1046
DOI: 10.4171/RMI/565

Published online: 2008-12-31

Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term

Sergio Polidoro[1] and Maria Alessandra Ragusa[2]

(1) Università di Bologna, Italy
(2) Università degli Studi di Catania, Italy

We prove a Harnack inequality for the positive solutions of ultraparabolic equations of the type $$ \mathcal {L}_0 u + \mathcal {V} u = 0, $$ where $\mathcal {L}_0$ is a linear second order hypoelliptic operator and $\mathcal {V}$ 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.

Keywords: Hypoelliptic operator, Schrödinger equation, Harnack inequality, Green function

Polidoro Sergio, Ragusa Maria Alessandra: Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term. Rev. Mat. Iberoamericana 24 (2008), 1011-1046. doi: 10.4171/RMI/565