Maximum principles for nonlinear integro-differential equations and symmetry of solutions

Pseudodifferential operators as generalizations of partial differential operators (35S05) Maximum principles in context of PDEs (35B50) Positive solutions to PDEs (35B09) Fractional partial differential equations (35R11) Integro-partial differential equations (35R09)

Cites Work

Regularity for fully nonlinear integro-differential operators with regularly varying kernels
A direct method of moving planes for the fractional Laplacian
Maximum principles for a fully nonlinear fractional order equation and symmetry of solutions
Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations
Classification of solutions of some nonlinear elliptic equations
Estimates on Green functions and Poisson kernels for symmetric stable processes
A priori estimates for prescribing scalar curvature equations
Maximum principles for the fractional p-Laplacian and symmetry of solutions
Local asymptotic symmetry of singular solutions to nonlinear elliptic equations
Obstacle problems for integro-differential operators: regularity of solutions and free boundaries
Liouville theorems involving the fractional Laplacian on a half space
A direct method of moving planes for the system of the fractional Laplacian
A direct method of moving spheres on fractional order equations
The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
Uniqueness of radial solutions for the fractional Laplacian
A concave-convex elliptic problem involving the fractional Laplacian
Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
An integral equation on half space
Regularity theory for fully nonlinear integro-differential equations
Regularity of harmonic functions for anisotropic fractional Laplacians
On the method of moving planes and the sliding method
Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian
The maximum principles for fractional Laplacian equations and their applications
RADIAL SYMMETRY OF POSITIVE SOLUTIONS TO EQUATIONS INVOLVING THE FRACTIONAL LAPLACIAN
An Extension Problem Related to the Fractional Laplacian
Classification of solutions for an integral equation
Symmetry via antisymmetric maximum principles in nonlocal problems of variable order

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