A priori estimates of solutions to nonlinear fractional Laplacian equation

被引：0

作者：

Zhang, Tao ^{[1
]}

Cheng, Tingzhi ^{[2
]}

机构：

[1] Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Peoples R China

[2] Ludong Univ, Sch Math & Stat Sci, Yantai 264025, Peoples R China

来源：

ELECTRONIC RESEARCH ARCHIVE | 2022年 / 31卷 / 02期

基金：

中国国家自然科学基金;

关键词：

a priori estimates; fractional Laplacian; nonlocal problems; PRESCRIBING SCALAR CURVATURE; ELLIPTIC-EQUATIONS; YAMABE PROBLEM; MOVING PLANES; S-N; COMPACTNESS; REGULARITY; SYMMETRY; MONOTONICITY; EXISTENCE;

D O I：

10.3934/era.2023056

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we focus on the research of a priori estimates of several types of semi-linear fractional Laplacian equations with a critical Sobolev exponent. Employing the method of moving planes, we can achieve a priori estimates which are closely connected to the existence of solutions to nonlinear fractional Laplacian equations. Our result can extend a priori estimates of the second order elliptic equation to the fractional Laplacian equation and we believe that the method used here will be applicable to more general nonlocal problems.

引用

页码：1119 / 1133

页数：15

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