COMPACTNESS AND GLOBAL ESTIMATES FOR A FOURTH ORDER EQUATION OF CRITICAL SOBOLEV GROWTH ARISING FROM CONFORMAL GEOMETRY

DOI10.1142/S0219199706002027zbMath1133.58027OpenAlexW2028971690MaRDI QIDQ5470152

Emmanuel Hebey, Yuliang Wen, Frédéric Robert

Publication date: 29 May 2006

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219199706002027

zbMATH Keywords

blow-upcritical exponentcompactnessfourth order operator

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Nonlinear elliptic equations (35J60) Variational principles in infinite-dimensional spaces (58E30) Elliptic equations on manifolds, general theory (58J05) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items

Quantization for a fourth order equation with critical exponential growth ⋮ Concentration phenomena for a fourth-order equation with exponential growth: the radial case ⋮ The Nirenberg problem and its generalizations: a unified approach ⋮ A non-compactness result on the fractional Yamabe problem in large dimensions ⋮ Variational analysis for nonlocal Yamabe-type systems ⋮ Non-compactness of the prescribed \(Q\)-curvature problem in large dimensions ⋮ Schrödinger-Poisson systems in the 3-sphere ⋮ Topological degree for solutions of fourth order mean field equations ⋮ Non-stability of Paneitz-Branson type equations in arbitrary dimensions ⋮ The Lin-Ni’s problem for mean convex domains ⋮ Existence results and a priori bounds for higher order elliptic equations and systems ⋮ On a fourth order Lichnerowicz type equation involving the Paneitz-Branson operator ⋮ Compactness and global estimates for the geometric Paneitz equation in high dimensions ⋮ Concentration phenomena for Liouville's equation in dimension four ⋮ MULTIPLE SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS ON COMPACT RIEMANNIAN MANIFOLDS ⋮ Asymptotic analysis for fourth order Paneitz equations with critical growth

Cites Work

• Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• A global compactness result for elliptic boundary value problems involving limiting nonlinearities
• Fourth order equations of critical Sobolev growth. Energy function and solutions of bounded energy in the conformally flat case
• Group representations arising from Lorentz conformal geometry
• The best constants problem in Sobolev inequalities
• 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
• Sharp Sobolev inequalities of second order
• Prescribing scalar curvature on \(S^ N\). I: A priori estimates.
• From one bubble to several bubbles: the low-dimensional case.
• Extremal metrics of zeta function determinants on 4-manifolds
• The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds
• Prescribed scalar curvature on the \(n\)-sphere
• The Yamabe problem on manifolds with boundary: Existence and compactness results
• Prescribing a higher order conformal invariant on \(S^n\)
• Critical exponents, critical dimensions and the biharmonic operator
• PRESCRIBING A FOURTH ORDER CONFORMAL INVARIANT ON THE STANDARD SPHERE — PART I: A PERTURBATION RESULT
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Elliptic Partial Differential Equations of Second Order
• YAMABE TYPE EQUATIONS ON THREE DIMENSIONAL RIEMANNIAN MANIFOLDS
• Blow-up examples for second order elliptic PDEs of critical Sobolev growth
• Positive solutions for a fourth order equation invariant under isometries
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
• Coercivity and Struwe's compactness for Paneitz type operators with constant coefficients