Symmetry of positive solutions for equations involving higher order fractional Laplacian

DOI10.1090/proc/13052zbMath1346.35215OpenAlexW2399264703MaRDI QIDQ2817008

Yan Li, Ran Zhuo

Publication date: 26 August 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/13052

zbMATH Keywords

equivalencerotational symmetrymethod of moving planesfractional Laplacianhigher-order fractional Laplacian

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Integral representations of solutions to PDEs (35C15) Positive solutions to PDEs (35B09) Fractional partial differential equations (35R11) Green's functions for elliptic equations (35J08)

Related Items (5)

Symmetric properties for system involving uniformly elliptic nonlocal operators ⋮ Symmetry of solutions for asymptotically symmetric nonlocal parabolic equations ⋮ A Liouville theorem for the higher-order fractional Laplacian ⋮ Conservative linearly-implicit difference scheme for a class of modified Zakharov systems with high-order space fractional quantum correction ⋮ Super poly-harmonic properties, Liouville theorems and classification of nonnegative solutions to equations involving higher-order fractional Laplacians

Cites Work

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• Liouville type theorems for poly-harmonic Navier problems
• A Liouville type theorem for poly-harmonic Dirichlet problems in a half space
• Hitchhiker's guide to the fractional Sobolev spaces
• Local integration by parts and Pohozaev identities for higher order fractional Laplacians
• On a fractional Henon equation and applications
• A system of integral equations on half space
• The Pohozaev identity for the fractional Laplacian
• Mountain pass solutions for non-local elliptic operators
• A characteristic property of spheres
• An integral system and the Lane-Emden conjecture
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Positive solutions of nonlinear problems involving the square root of the Laplacian
• Heat kernel estimates for the Dirichlet fractional Laplacian
• Comparison results and steady states for the Fujita equation with fractional Laplacian.
• Qualitative properties of solutions for an integral equation
• Gradient estimates for harmonic and \(q\)-harmonic functions of symmetric stable processes.
• Heat kernel estimates for the fractional Laplacian with Dirichlet conditions
• The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
• Liouville type theorems for Schrödinger system with Navier boundary conditions in a half space
• Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
• A Liouville type theorem for an integral system
• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
• Harmonic Function Theory
• A Liouville theorem for non local elliptic equations
• Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations
• Regularity of the obstacle problem for a fractional power of the laplace operator
• An integral equation on half space
• Euler Equations, Navier-Stokes Equations and Turbulence
• Regularity theory for fully nonlinear integro-differential equations
• Lévy Processes and Stochastic Calculus
• A gradient bound and a liouville theorem for nonlinear poisson equations
• Classification of Solutions for a System of Integral Equations
• Financial Modelling with Jump Processes
• On the method of moving planes and the sliding method
• SOBOLEV INEQUALITIES WITH SYMMETRY
• An Extension Problem Related to the Fractional Laplacian
• Classification of solutions for an integral equation
• Monotonicity and nonexistence results for some fractional elliptic problems in the half-space
• Symmetry via antisymmetric maximum principles in nonlocal problems of variable order

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