Work

Classification of solutions to equations involving higher-order fractional Laplacian

Year: 2025

Type: article

Abstract: We study the following equation involving higher-order fractional Laplacian: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. Under either one of the two integral constraints [Formula: see text] and [Formula: see text] we establish an integral representation formula for any nonconstant classical solution satisfying certain growth at infinity. From this, we prove that these solutions are radially symmetric about some point in [Formula: see text] and monotone decreasing in the radial direction via method of moving planes in integral forms. We also establish a Moser–Trudinger-type inequality associated to the equation [Formula: see text] in bounded domain for [Formula: see text].

Source: Analysis and Applications

DOI: 10.1142/s0219530525500149

Authors: Zhuoran Du, Zhenping Feng, Jiaqi Hu, Yuan Li

Institutions: Hunan University, Henan Normal University, PLA Information Engineering University, East China Normal University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: China Postdoctoral Science Foundation, Science and Technology Commission of Shanghai Municipality, Natural Science Foundation of Hainan Province

Awards: G1599855015, G1609915050, G7748632204