Liouville theorem for poly-harmonic functions on R+n

Wei Dai; Guolin Qin

doi:10.1007/s00013-020-01464-1

Liouville theorem for poly-harmonic functions on R+n

Wei Dai
, Guolin Qin^*

^*此作品的通讯作者

数学科学学院

Université Paris 13
Chinese Academy of Sciences
University of Chinese Academy of Sciences

科研成果: 期刊稿件 › 文章 › 同行评审

7 引用（Scopus）

摘要

In this paper, we will prove a Liouville theorem for poly-harmonic functions on R+n with Navier boundary conditions, that is, the nonnegative poly-harmonic functions u satisfying u(x) = o(| x| ³) at ∞ must assume the form u(x)=Cxnin R+n¯, where n≥ 2 and C is a nonnegative constant. The assumption u(x) = o(| x| ³) at ∞ is optimal for us to derive the super poly-harmonic properties of u.

源语言	英语
页（从-至）	317-327
页数	11
期刊	Archiv der Mathematik
卷	115
期	3
DOI	https://doi.org/10.1007/s00013-020-01464-1
出版状态	已出版 - 1 9月 2020

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title = "Liouville theorem for poly-harmonic functions on R+n",

abstract = "In this paper, we will prove a Liouville theorem for poly-harmonic functions on R+n with Navier boundary conditions, that is, the nonnegative poly-harmonic functions u satisfying u(x) = o(| x| 3) at ∞ must assume the form u(x)=Cxnin R+n¯, where n≥ 2 and C is a nonnegative constant. The assumption u(x) = o(| x| 3) at ∞ is optimal for us to derive the super poly-harmonic properties of u.",

keywords = "Harmonic asymptotic expansions, Liouville theorems, Navier problems, Poly-harmonic functions, Super poly-harmonic properties",

author = "Wei Dai and Guolin Qin",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.",

year = "2020",

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T1 - Liouville theorem for poly-harmonic functions on R+n

AU - Dai, Wei

AU - Qin, Guolin

PY - 2020/9/1

Y1 - 2020/9/1

N2 - In this paper, we will prove a Liouville theorem for poly-harmonic functions on R+n with Navier boundary conditions, that is, the nonnegative poly-harmonic functions u satisfying u(x) = o(| x| 3) at ∞ must assume the form u(x)=Cxnin R+n¯, where n≥ 2 and C is a nonnegative constant. The assumption u(x) = o(| x| 3) at ∞ is optimal for us to derive the super poly-harmonic properties of u.

AB - In this paper, we will prove a Liouville theorem for poly-harmonic functions on R+n with Navier boundary conditions, that is, the nonnegative poly-harmonic functions u satisfying u(x) = o(| x| 3) at ∞ must assume the form u(x)=Cxnin R+n¯, where n≥ 2 and C is a nonnegative constant. The assumption u(x) = o(| x| 3) at ∞ is optimal for us to derive the super poly-harmonic properties of u.

KW - Harmonic asymptotic expansions

KW - Liouville theorems

KW - Navier problems

KW - Poly-harmonic functions

KW - Super poly-harmonic properties

UR - https://www.scopus.com/pages/publications/85083772550

U2 - 10.1007/s00013-020-01464-1

DO - 10.1007/s00013-020-01464-1

M3 - 文章

AN - SCOPUS:85083772550

SN - 0003-889X

VL - 115

SP - 317

EP - 327

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 3

ER -

Liouville theorem for poly-harmonic functions on R+n

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