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Theorems of the Phragmén–Lindelöf Type for Subfunctions in a Cone

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  29 December 2016

Lei Qiao  and
Guoshuang Pan
Lei Qiao*
Affiliation:
Laboratoire de Mathématiques de Bretagne Atlantique, UMR 6205, Université de Bretagne-Sud, Vannes 56000, France (lei.quiao@univ-ubs.fr)
Guoshuang Pan
Affiliation:
Beijing National Day School, 66 Yuquan Rd, Haidian Qu, Beijing 100039, People's Republic of China
*
†Corresponding author.
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Abstract

Our first aim in this paper is to deal with the maximum principle for subfunctions in an arbitrary unbounded domain. As an application, we next give a result concerning the classical Phragmén–Lindelöf theorem for subfunctions in a cone. For a subfunction defined in a cone that is dominated on the boundary by a certain function, we finally generalize the Phragmén–Lindelöf type theorem by making a generalized harmonic majorant of it.

Keywords

stationary Schrödinger operatorPoisson–Sch integralPhragmén–Lindelöfcone

MSC classification

Secondary: 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation 35J10: Schrödinger operator
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 3 , August 2017 , pp. 739 - 751
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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Footnotes

*

Present address: School of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450046, People's Republic of China (qiaocqu@163.com).

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