Advances in Differential Equations

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

Sergio Polidoro and Maria Alessandra Ragusa

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Permanent link to this document
https://projecteuclid.org/euclid.ade/1356651611

Mathematical Reviews number (MathSciNet)
MR1920683

Zentralblatt MATH identifier
1207.35200

Subjects
Primary: 35K70: Ultraparabolic equations, pseudoparabolic equations, etc.
Secondary: 35A08: Fundamental solutions 35B45: A priori estimates 35B65: Smoothness and regularity of solutions

Citation

Polidoro, Sergio; Ragusa, Maria Alessandra. A Green function and regularity results for an ultraparabolic equation with a singular potential. Adv. Differential Equations 7 (2002), no. 11, 1281--1314. https://projecteuclid.org/euclid.ade/1356651611.


Export citation