A Liouville theorem for the higher-order fractional Laplacian

DOI10.1142/S0219199718500050zbMath1411.35057arXiv1609.04105OpenAlexW3100117745MaRDI QIDQ4630362

Ran Zhuo, Yan Li

Publication date: 26 March 2019

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.04105

zbMATH Keywords

symmetrynonexistencemethod of moving planes

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Maximum principles in context of PDEs (35B50) Fractional partial differential equations (35R11) Green's functions for elliptic equations (35J08) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (7)

Symmetry and nonexistence of positive solutions for an elliptic system involving the Fractional Laplacian ⋮ Fractional \(p\)-Laplacian problems with negative powers in a ball or an exterior domain ⋮ Liouville theorem for Hénon-Hardy systems in the unit ball ⋮ On a super polyharmonic property of a higher-order fractional Laplacian ⋮ Liouville type theorems for fractional and higher-order fractional systems ⋮ Sliding methods for the higher order fractional Laplacians ⋮ Symmetry and nonexistence results for a fractional Hénon-Hardy system on a half-space

Cites Work

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• Symmetry and non-existence of solutions for a nonlinear system involving the fractional Laplacian
• A direct method of moving planes for the fractional Laplacian
• Nonexistence of positive solutions for a semi-linear equation involving the fractional Laplacian in \(\mathbb{R}^n\)
• A priori estimates and existence of positive solutions of semilinear elliptic equations
• Symmetry of solutions for a fractional system
• Regularity of solutions for a system of integral equations
• Heat kernel estimates for the fractional Laplacian with Dirichlet conditions
• Some Liouville theorems for the fractional Laplacian
• Liouville theorems involving the fractional Laplacian on a half space
• Liouville type theorems for Schrödinger system with Navier boundary conditions in a half space
• A Liouville type theorem for an integral system
• Entire $s$-harmonic functions are affine
• A direct blowing-up and rescaling argument on nonlocal elliptic equations
• Symmetry of positive solutions for equations involving higher order fractional Laplacian
• Global heat kernel estimates for symmetric jump processes
• Non-local Dirichlet forms and symmetric jump processes
• Classification of Solutions for a System of Integral Equations
• Classification of solutions for an integral equation

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