Advances in Differential Equations

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

Sergio Polidoro and Maria Alessandra Ragusa

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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


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