Sharp subcritical Sobolev inequalities and uniqueness of nonnegative solutions to high-order Lane-Emden equations on \(\mathbb{S}^n\)
DOI10.3934/cpaa.2022073OpenAlexW3181301824MaRDI QIDQ2087554
Guozhen Lu, Lu Chen, Yansheng Shen
Publication date: 21 October 2022
Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2107.04884
extremal functionssharp constantsLane-Emden equationsmoving-plane methoduniqueness of nonnegative solutionsGJMS operators on \(\mathbb{S}^n\)
Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Symmetries, invariants, etc. in context of PDEs (35B06) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Cites Work
- Explicit formulas for GJMS-operators and \(Q\)-curvatures
- Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
- Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
- The concentration-compactness principle in the calculus of variations. The limit case. I
- A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds (Summary)
- Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
- An integral equation in conformal geometry
- Classification of solutions of some nonlinear elliptic equations
- Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
- Best constant in Sobolev inequality
- Problèmes isoperimetriques et espaces de Sobolev
- Classification of solutions of higher order conformally invariant equations
- A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
- On conformally invariant equation \((-\Delta)^p u-K(x)u^{\frac{N+2p}{N-2p}}=0\) and its generalizations
- Paneitz-type operators and applications
- Best constants for Sobolev inequalities for higher order fractional derivatives
- Stein-Weiss inequalities with the fractional Poisson kernel
- Reverse Stein-Weiss inequalities on the upper half space and the existence of their extremals
- Best constant for the embedding of the space \(H^ 2\cap H^ 1_ 0(\Omega)\) into \(L^{2N/(N-4)}\Omega\)
- Reversed Stein-Weiss inequalities with Poisson-type kernel and qualitative analysis of extremal functions
- Conformally Invariant Powers of the Laplacian, I: Existence
- Conformally Invariant Powers of the Laplacian, II: Nonexistence
- The best sobolev constant
- Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
- ON THE HIGHER ORDER CONFORMAL COVARIANT OPERATORS ON THE SPHERE
- Differential operators cononically associated to a conformal structure.
- Global and local behavior of positive solutions of nonlinear elliptic equations
- Conformally invariant powers of the Laplacian — A complete nonexistence theorem
- Reverse Stein–Weiss inequalities and existence of their extremal functions
- Sharp constant in a Sobolev inequality
- Juhl’s formulae for GJMS operators and $Q$-curvatures
- Classification of solutions for an integral equation
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