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

被引：0

作者：

Wang, Junqing ^{[1
]}

Wang, Liping ^{[2
]}

机构：

[1] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China

[2] East China Normal Univ, Sch Math Sci, Key Lab MEA, Shanghai Key Lab PMMP,Minist Educ, Shanghai 200241, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2025年

基金：

上海市自然科学基金;

关键词：

Monotonicity formula; stable solutions; Joseph-Lundgren exponent; Liouville-type theorem; CLASSIFICATION;

D O I：

10.3934/cpaa.2025031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：1179 / 1202

页数：24

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