Mean field equations of Liouville type with singular data: sharper estimates

DOI10.3934/dcds.2010.28.1237zbMath1211.35263OpenAlexW2017823236MaRDI QIDQ983484

Chang-Shou Lin, Chuin Chuan Chen

Publication date: 23 July 2010

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2010.28.1237

zbMATH Keywords

blow-updegree theorysingular solutionLiouville equationmean field equationChen-Simons-Higgs equation

Mathematics Subject Classification ID

Other nonlinear integral equations (45G10) Nonlinear elliptic equations (35J60) Integro-partial differential equations (35R09)

Related Items (51)

Mean field equation and relativistic Abelian Chern-Simons model on finite graphs ⋮ Existence of mixed type solutions in the Chern-Simons gauge theory of rank two in \(\mathbb{R}^2\) ⋮ Compactness, existence and multiplicity for the singular mean field problem with sign-changing potentials ⋮ Singular limits for Liouville-type equations on the flat two-torus ⋮ Blow-up analysis for a cosmic strings equation ⋮ An improved geometric inequality via vanishing moments, with applications to singular Liouville equations ⋮ A Morse index formula for radial solutions of Lane-Emden problems ⋮ Local uniqueness and non-degeneracy of blow up solutions of mean field equations with singular data ⋮ Singular limits solution for two-dimensional elliptic problems involving exponential nonlinearities with nonlinear gradient terms and singular weights ⋮ On Liouville systems at critical parameters. I: One bubble ⋮ Existence of bubbling solutions for the Liouville system in a torus ⋮ Sharp estimates for fully bubbling solutions of \(B_2\) Toda system ⋮ A generalized mean field type flow on a closed Riemann surface ⋮ Uniqueness of bubbling solutions with collapsing singularities ⋮ Existence of bubbling solutions without mass concentration ⋮ A priori estimates for \(D_4\) and \(F_4\) Toda systems ⋮ When ``blow-up does not imply ``concentration: a detour from Brézis-Merle's result ⋮ On the asymptotics for minimizers of Donaldson functional in Teichmüller theory ⋮ Sharp estimates for solutions of mean field equations with collapsing singularity ⋮ Estimates of Bubbling Solutions of $SU(3)$ Toda Systems at Critical Parameters. Part 1 ⋮ Liouville systems of mean field equations ⋮ Classification of radial solutions to Liouville systems with singularities ⋮ Doubly periodic self-dual vortices in a relativistic non-abelian Chern-Simons model ⋮ Weighted barycentric sets and singular Liouville equations on compact surfaces ⋮ Uniqueness of bubbling solutions of mean field equations ⋮ Bifurcation for minimal surface equation in hyperbolic 3-manifolds ⋮ Sharp asymptotic behavior of radial solutions of some planar semilinear elliptic problems ⋮ Asymptotic blow-up analysis for singular Liouville type equations with applications ⋮ Theory of ``critical points at infinity and a resonant singular Liouville-type equation ⋮ Singular limit solutions for a 2-dimensional semilinear elliptic system of Liouville type in some general case adding singular sources. I ⋮ Exact Morse index computation for nodal radial solutions of Lane-Emden problems ⋮ Degree counting and shadow system for Toda system of rank two: one bubbling ⋮ Non-degeneracy and uniqueness of solutions to singular mean field equations on bounded domains ⋮ Nondegeneracy of the Gauss curvature equation with negative conic singularity ⋮ Classification and nondegeneracy of \(SU(n+1)\) Toda system with singular sources ⋮ Relativistic Chern–Simons–Higgs vortex equations ⋮ Weighted Trudinger-Moser inequalities and associated Liouville type equations ⋮ Degree counting for Toda system with simple singularity: one point blow up ⋮ Sharp estimate for the critical parameters of \(SU(3)\) Toda system with arbitrary singularities. I ⋮ Local profile of fully bubbling solutions to \(\mathrm {SU} (n+1)\) Toda systems ⋮ On the topological degree of the mean field equation with two parameters ⋮ Singular mean field equations on compact Riemann surfaces ⋮ Morse index computation for radial solutions of the Hénon problem in the disk ⋮ Mean field equations on tori: existence and uniqueness of evenly symmetric blow-up solutions ⋮ A singular sphere covering inequality: uniqueness and symmetry of solutions to singular Liouville-type equations ⋮ Construction of nodal bubbling solutions for the weighted sinh-Poisson equation ⋮ Blow up at infinity in the SU(3) Chern-Simons model, part I ⋮ Mean Field Equation of Liouville Type with Singular Data: Topological Degree ⋮ Uniqueness of bubbling solutions of mean field equations with non-quantized singularities ⋮ On the Ambjorn-Olesen electroweak condensates ⋮ Supercritical mean field equations on convex domains and the Onsager's statistical description of two-dimensional turbulence

This page was built for publication: Mean field equations of Liouville type with singular data: sharper estimates