Positive solutions for a fourth order equation invariant under isometries

DOI10.1090/S0002-9939-02-06676-5zbMath1112.58037MaRDI QIDQ4791484

Frédéric Robert

Publication date: 28 January 2003

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

positive solutionvariational methodfourth order elliptic equationinvariant solutioninvariant conformal metric

Mathematics Subject Classification ID

Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (13)

Multiple solutions to singular fourth order elliptic equations on compact manifolds ⋮ Large singular solutions for conformal \(Q\)-curvature equations on \(\mathbb{S}^n\) ⋮ A note on prescribed Q-curvature ⋮ The Nirenberg problem and its generalizations: a unified approach ⋮ Nodal solutions for fourth order elliptic equations with critical exponent on compact manifolds ⋮ Existence of solutions to a conformally invariant integral equation involving Poisson-type kernels ⋮ Sharp Sobolev inequalities of second order ⋮ The Paneitz equation in hyperbolic space ⋮ Asymptotic Profile for a Fourth Order PDE with Critical Exponential Growth in Dimension Four ⋮ Concentration phenomena for Liouville's equation in dimension four ⋮ GJMS-type operators on a compact Riemannian manifold: best constants and Coron-type solutions ⋮ COMPACTNESS AND GLOBAL ESTIMATES FOR A FOURTH ORDER EQUATION OF CRITICAL SOBOLEV GROWTH ARISING FROM CONFORMAL GEOMETRY ⋮ Asymptotic in Sobolev spaces for symmetric Paneitz-type equations on Riemannian manifolds

Cites Work

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• A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds (Summary)
• Conformal metrics with prescribed scalar curvature
• Group representations arising from Lorentz conformal geometry
• The best constants problem in Sobolev inequalities
• Paneitz-type operators and applications
• Critical exponents, critical dimensions and the biharmonic operator
• Coercivity and Struwe's compactness for Paneitz type operators with constant coefficients

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