A few symmetry results for nonlinear elliptic PDE on noncompact manifolds

DOI10.1016/S0294-1449(01)00091-9zbMath1029.35096OpenAlexW1983161195WikidataQ125363524 ScholiaQ125363524MaRDI QIDQ1865027

Yanyan Li

Publication date: 23 March 2003

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_2002__19_3_313_0

zbMATH Keywords

method of moving planesSobolev inequalitiesgrowth conditionsgeometric properties of the manifoldvariatonal technique

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Nonlinear elliptic equations (35J60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for elliptic systems (35J50) Elliptic equations on manifolds, general theory (58J05)

Related Items

Hardy-Sobolev inequalities in half-space and some semilinear elliptic equations with singular coefficients, SYMMETRY AND EXISTENCE OF SOLUTIONS OF SEMI-LINEAR ELLIPTIC SYSTEMS IN HYPERBOLIC SPACE, Some rigidity results for Sobolev inequalities and related PDEs on Cartan-Hadamard manifolds, Potential characterizations of geodesic balls on hyperbolic spaces: a moving plane approach, Classification for positive solutions of degenerate elliptic system, Stability and qualitative properties of radial solutions of the Lane-Emden-Fowler equation on Riemannian models, High frequency periodic solutions of semilinear equations, NON-EXISTENCE, MONOTONICITY FOR POSITIVE SOLUTIONS OF SEMILINEAR ELLIPTIC SYSTEM IN $\mathbb{R}_+^N$, Singly periodic solutions of a semilinear equation, Hardy-Sobolev inequalities and hyperbolic symmetry, Liouville Type Theorems for Positive Solutions of Elliptic System in ℝ^N, Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models, Kirchhoff-type problems on a geodesic ball of the hyperbolic space, Nondegeneracy of positive solutions of semilinear elliptic problems in the hyperbolic space, Higher order Brezis-Nirenberg problem on hyperbolic spaces: existence, nonexistence and symmetry of solutions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Symmetry and related properties via the maximum principle
• Symmetry of ground states of quasilinear elliptic equations
• Symmetry of ground states of \(p\)-Laplace equations via the moving plane method
• Sobolev spaces on Riemannian manifolds
• Symmetry properties of positive solutions to some elliptic equations with nonlinear boundary conditions
• On positive entire solutions to a class of equations with a singular coefficient and critical exponent
• Inequalities for second-order elliptic equations with applications to unbounded domains. I
• Symmetry results for positive solutions of some elliptic equations on manifolds
• A symmetry problem in potential theory
• Symmetry of C¹ Solutions of p-Laplace Equations in ℝ^N
• Radial symmetry of positive solutions of nonlinear elliptic equations in Rⁿ
• Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domains
• On the method of moving planes and the sliding method