Uniqueness theorems through the method of moving spheres

1995/11/01 by Yanyan Li, Meijun Zhu, Mei‐Jun Zhu · 28 citations
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows

paper · doi:10.1215/s0012-7094-95-08016-8

Citations

• Classification of solutions of some nonlinear elliptic equations
• A symmetry problem in potential theory
• Global and local behavior of positive solutions of nonlinear elliptic equations
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth

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• Sharp integral inequalities for harmonic functions
• Liouville-type theorems, radial symmetry and integral representation of solutions to Hardy-Hénon equations involving higher order fractional Laplacians
• Uniqueness results for positive harmonic functions on manifolds with nonnegative Ricci curvature and strictly convex boundary
• Isolated singularities of solutions to the Yamabe equation in dimension 6
• Extremal functions for a class of trace Trudinger-Moser inequalities
• Compactness of scalar-flat conformal metrics on low-dimensional manifolds with constant mean curvature on boundary
• On a new region for the Lane-Emden conjecture in higher dimensions
• Existence and Nonexistence Breaking Results For a Weighted Elliptic Problem in Half-Space
• From fractional Lane-Emden-Serrin equation -- existence, multiplicity and local behaviors via classical ODE -- to fractional Yamabe metrics with singularity of "maximal" dimension
• Prescribing Gaussian and geodesic curvature on disks
• Liouville type theorem for a class of quasilinear p-Laplace type equations in the half space
• Maximum principles and monotonicity of solutions for fractional p-equations in unbounded domains
• A nonlinear Liouville theorem for fractional equations in the Heisenberg group
• Existence of conformal metrics with constant scalar curvature and constant boundary mean curvature on compact manifolds
• Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries
• The local behavior of positive solutions for higher order equation with isolated singularity
• Critical Exponent Elliptic Equations on the Half-Space: Uniqueness and Explicit Solutions
• Asymptotic behavior of solutions for nonlinear elliptic problems with\n the fractional Laplacian
• Uniqueness results for positive harmonic functions on \mathbbBⁿ satisfying a nonlinear boundary condition
• Multi-bump solutions for fractional Nirenberg problem
• Liouville theorems for fractional parabolic equations
• Classification of finite energy solutions to the fractional Lane-Emden-Fowler equations with slightly subcritical exponents