Uniqueness and symmetry results for solutions of a mean field equation on 𝕊2 via a new bubbling phenomenon

DOI10.1002/cpa.20385zbMath1250.58009OpenAlexW2002289496MaRDI QIDQ3100891

Daniele Bartolucci, Chang-Shou Lin, Grabriella Tarantello

Publication date: 22 November 2011

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cpa.20385

zbMATH Keywords

moving planes methodconcentration phenomenonAlexandrov-Bol inequality

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05)

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Cites Work

• Unnamed Item
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• On the classification of \(N\)-points concentrating solutions for mean field equations and the symmetry properties of the \(N\)-vortex singular Hamiltonian on the unit disk
• Analytical, geometrical and topological aspects of a class of mean field equations on surfaces
• Multiplicity results for the assigned Gauss curvature problem in \(\mathbb R^2\)
• Harnack type inequality: The method of moving planes
• Qualitative properties of solutions to some nonlinear elliptic equations in \(\mathbb{R}^2\)
• On the asymptotic behavior of solutions of the conformal Gaussian curvature equations in \(\mathbb R^ 2\)
• Construction of singular limits for a semilinear elliptic equation in dimension 2
• Uniqueness of solutions to the mean field equations for the spherical Onsager vortex
• Topological degree for mean field equations on \(S^2\)
• A quantization property for blow up solutions of singular Liouville-type equations
• On the existence of blowing-up solutions for a mean field equation
• Liouville type equations with singular data and their applications to periodic multivortices for the electroweak theory
• Singular limits in Liouville-type equations
• On a class of elliptic problems in R²: symmetry and uniqueness results
• BLOW-UP ANALYSIS FOR LIOUVILLE TYPE EQUATION IN SELF-DUAL GAUGE FIELD THEORIES
• Profile of Blow-up Solutions to Mean Field Equations with Singular Data
• On the shape of blow-up solutions to a mean field equation
• Uniqueness Results for Mean Field Equations with Singular Data
• Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)e^uin two dimensions
• Topological degree for a mean field equation on Riemann surfaces
• Sharp estimates for solutions of multi‐bubbles in compact Riemann surfaces
• Blowup Solutions for a Liouville Equation with Singular Data
• Blow‐up analysis, existence and qualitative properties of solutions for the two‐dimensional Emden–Fowler equation with singular potential
• The existence of non-topological multivortex solutions in the relativistic self-dual Chern-Simons theory
• On the symmetry of blowup solutions to a mean field equation