MONOTONICITY FORMULA AND LIOUVILLE-TYPE THEOREM FOR STABLE SOLUTIONS OF WEIGHTED FOURTH ORDER ELLIPTIC EQUATION

Junqing Wang; Liping Wang

doi:10.3934/cpaa.2025031

MONOTONICITY FORMULA AND LIOUVILLE-TYPE THEOREM FOR STABLE SOLUTIONS OF WEIGHTED FOURTH ORDER ELLIPTIC EQUATION

Junqing Wang
, Liping Wang^*

^*此作品的通讯作者

数学科学学院

Nankai University

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

In this paper we consider some weighted fourth-order elliptic equation arising from a conical metric on singular manifolds. For such generalized equation, we derive the monotonicity formula and obtain the Liouville-type result for stable solutions with blow-down analysis. Moreover, we obtain the explicit expression of the corresponding Joseph-Lundgren exponent and a type of weighted Hardy-Rellich inequality with optimal constant.

源语言	英语
页（从-至）	1179-1202
页数	24
期刊	Communications on Pure and Applied Analysis
卷	24
期	7
DOI	https://doi.org/10.3934/cpaa.2025031
出版状态	已出版 - 7月 2025

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title = "MONOTONICITY FORMULA AND LIOUVILLE-TYPE THEOREM FOR STABLE SOLUTIONS OF WEIGHTED FOURTH ORDER ELLIPTIC EQUATION",

abstract = "In this paper we consider some weighted fourth-order elliptic equation arising from a conical metric on singular manifolds. For such generalized equation, we derive the monotonicity formula and obtain the Liouville-type result for stable solutions with blow-down analysis. Moreover, we obtain the explicit expression of the corresponding Joseph-Lundgren exponent and a type of weighted Hardy-Rellich inequality with optimal constant.",

keywords = "Joseph-Lundgren exponent, Liouville-type theorem, Monotonicity formula, stable solutions",

author = "Junqing Wang and Liping Wang",

year = "2025",

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doi = "10.3934/cpaa.2025031",

language = "英语",

volume = "24",

pages = "1179--1202",

journal = "Communications on Pure and Applied Analysis",

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AU - Wang, Junqing

AU - Wang, Liping

PY - 2025/7

Y1 - 2025/7

N2 - In this paper we consider some weighted fourth-order elliptic equation arising from a conical metric on singular manifolds. For such generalized equation, we derive the monotonicity formula and obtain the Liouville-type result for stable solutions with blow-down analysis. Moreover, we obtain the explicit expression of the corresponding Joseph-Lundgren exponent and a type of weighted Hardy-Rellich inequality with optimal constant.

AB - In this paper we consider some weighted fourth-order elliptic equation arising from a conical metric on singular manifolds. For such generalized equation, we derive the monotonicity formula and obtain the Liouville-type result for stable solutions with blow-down analysis. Moreover, we obtain the explicit expression of the corresponding Joseph-Lundgren exponent and a type of weighted Hardy-Rellich inequality with optimal constant.

KW - Joseph-Lundgren exponent

KW - Liouville-type theorem

KW - Monotonicity formula

KW - stable solutions

UR - https://www.scopus.com/pages/publications/86000573921

U2 - 10.3934/cpaa.2025031

DO - 10.3934/cpaa.2025031

M3 - 文章

AN - SCOPUS:86000573921

SN - 1534-0392

VL - 24

SP - 1179

EP - 1202

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 7

ER -

MONOTONICITY FORMULA AND LIOUVILLE-TYPE THEOREM FOR STABLE SOLUTIONS OF WEIGHTED FOURTH ORDER ELLIPTIC EQUATION

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