Sliding Methods for a Class of Generalized Fractional Laplacian Equations

被引：0
作者：
Miao Sun
Baiyu Liu
机构：
[1] University of Science and Technology Beijing,School of Mathematics and Physics
来源：
Bulletin of the Malaysian Mathematical Sciences Society | 2022年 / 45卷
关键词：
Sliding method; Generalized fractional Laplacian; Monotonicity; Approximate maximum points technique; 35R11; 35B07;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper deals with the monotonicity of solutions for equations driven by a class of generalized fractional Laplacian, which is related to fractional magnetic Laplacian. By applying the direct sliding method together with the maximum principle for small domains, we obtain a monotonicity result for solutions of the generalized fractional Laplacian equations in bounded domains. Then, we use the direct sliding method to establish a monotonicity result in the whole space, in which a key ingredient is the approximate maximum points technique.
引用
收藏
页码：2225 / 2247
页数：22
相关论文
共 60 条
[1]  
D’Avenia P(2018)Ground states for fractional magnetic operators ESAIM Control Optim. Calc. Var. 24 1-24
[2]  
Squassina M(1988)Monotonicity, symmetry and anti-symmetry of solutions of semi-linear elliptic equations J. Geom. Phys. 5 237-275
[3]  
Berestycki H(1991)On the method of moving planes and the sliding method B. Braz. Math. Soc. 22 1-37
[4]  
Nirenberg L(2007)An extension problem related to the fractional Laplacian Commun. Part. Differ. Equ. 32 1245-1260
[5]  
Berestycki H(2020)The sliding method for the nonlocal Monge–Ampere operator Nonlinear Anal. 196 735-758
[6]  
Nirenberg L(2018)Maximum principles for the fractional p-Laplacian and symmetry of solutions Adv. Math. 335 404-437
[7]  
Caffarelli L(2017)A direct method of moving planes for the fractional Laplacian Adv. Math. 308 29-4157
[8]  
Silvestre L(2017)Maximum principles for a fully nonlinear fractional order equation and symmetry of solutions Calc. Var. 56 4131-65
[9]  
Chen X(2017)A direct method of moving spheres on fractional order equations J. Funct. Anal. 272 59-354
[10]  
Bao G(2005)Classification of solutions for a system of integral equations Commun. Part. Differ. Equ. 30 347-343
123456