Existence of solutions to a higher dimensional mean-field equation on manifolds

DOI10.1007/S00229-010-0365-1zbMath1198.35092arXiv1001.5231OpenAlexW2028523270MaRDI QIDQ993394

Luca Martinazzi, Mircea Petrache

Publication date: 10 September 2010

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.5231

zbMATH Keywords

Riemannian manifoldLaplace-Beltrami operatormean-field equation

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Elliptic equations on manifolds, general theory (58J05) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Variational methods for higher-order elliptic equations (35J35)

Cites Work

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• Classification of solutions to the higher order Liouville's equation on \({\mathbb{R}^{2m}}\)
• Concentration-compactness phenomena in the higher order Liouville's equation
• Morse theory and a scalar field equation on compact surfaces
• The existence of surfaces of constant mean curvature with free boundaries
• A sharp inequality of J. Moser for higher order derivatives
• Existence results for mean field equations
• Sharp borderline Sobolev inequalities on compact Riemannian manifolds
• Constant \(Q\)-curvature metrics in arbitrary dimension
• Concentration phenomena for Liouville's equation in dimension four
• EXISTENCE RESULT FOR THE MEAN FIELD PROBLEM ON RIEMANN SURFACES OF ALL GENUSES
• Asymptotics and Quantization for a Mean-Field Equation of Higher Order
• Multiplicity Result for a Scalar Field Equation on Compact Surfaces
• Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)e^uin two dimensions
• Compactness of solutions to some geometric fourth-order equations
• Bubbling phenomena for fourth-order four-dimensional PDEs with exponential growth

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