MONOTONICITY OF SOLUTIONS FOR WEIGHTED FRACTIONAL PARABOLIC EQUATIONS ON THE UPPER HALF SPACE

被引：4

作者：

Lin, Chuang ^{[1
]}

Dou, Jingbo ^{[1
]}

机构：

[1] Shaanxi Normal Univ, Sch Math & Stat, Xian 710119, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2023年 / 22卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Weighted fractional Laplacian; parabolic equation; monotonicity; max-imum principle of antisymmetric functions; narrow region principle; Hopf lemma; method of mov-ing planes; REGULARITY; SYMMETRY; THEOREMS;

D O I：

10.3934/cpaa.2023067

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the monotonicity of positive solutions for the weighted fractional parabolic equations on the upper half space. Firstly, by choosing and estimating appropriate auxiliary functions, we establish the narrow region principle, the maximum principle and Hopf lemma of antisymmetric functions. And then we show the strictly monotonicity of solutions for parabolic equations on the upper half space via the method of moving planes. As an application, we show the existence of positive bounded solutions for parabolic equations related to the weighted fractional parabolic equations on the whole space.

引用

页码：2298 / 2320

页数：23

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