Translator Disclaimer
September/October 2017 Positive solutions of Schrödinger equations and Martin boundaries for skew product elliptic operators
Minoru Murata, Tetsuo Tsuchida
Adv. Differential Equations 22(9/10): 621-692 (September/October 2017).

Abstract

We consider positive solutions of elliptic partial differential equations on non-compact domains of Riemannian manifolds. We establish general theorems which determine Martin compactifications and Martin kernels for a wide class of elliptic equations in skew product form, by thoroughly exploiting parabolic Martin kernels for associated parabolic equations developed in [35] and [25]. As their applications, we explicitly determine the structure of all positive solutions to a Schrödinger equation and the Martin boundary of the product of Riemannian manifolds. For their sharpness, we show that the Martin compactification of ${\mathbb R}^2$ for some Schrödinger equation is so much distorted near infinity that no product structures remain.

Citation

Download Citation

Minoru Murata. Tetsuo Tsuchida. "Positive solutions of Schrödinger equations and Martin boundaries for skew product elliptic operators." Adv. Differential Equations 22 (9/10) 621 - 692, September/October 2017.

Information

Published: September/October 2017
First available in Project Euclid: 27 May 2017

zbMATH: 1376.35015
MathSciNet: MR3656489

Subjects:
Primary: 31C12, 31C35, 35B09, 35C15, 35J08, 35K08

Rights: Copyright © 2017 Khayyam Publishing, Inc.

JOURNAL ARTICLE
72 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.22 • No. 9/10 • September/October 2017
Back to Top