On rank-2 Toda systems with arbitrary singularities: local mass and new estimates

DOI10.2140/apde.2018.11.873zbMath1383.35078arXiv1609.02772OpenAlexW3104708691MaRDI QIDQ1692137

Chang-Shou Lin, Wen Yang, Lei Zhang, Wei, Juncheng

Publication date: 26 January 2018

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.02772

zbMATH Keywords

blowup solutionsrank-2 Toda systems

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Second-order elliptic systems (35J47)

Related Items (18)

On the blow-up analysis at collapsing poles for solutions of singular Liouville-type equations ⋮ Degree counting formula for non-symmetric Toda systems of rank two ⋮ The \(\operatorname{SU}(3)\) Toda system with multiple singular sources ⋮ Sharp upper bound of the number of solutions for the \(\mathrm{SU} (N + 1)\) Toda system on torus with non-critical parameters ⋮ Existence of bubbling solutions without mass concentration ⋮ A priori estimates for \(D_4\) and \(F_4\) Toda systems ⋮ On the general Toda system with multiple singular points ⋮ Estimates of bubbling sequences of SU(3)$SU(3)$ Toda systems at critical parameters: Part 2 ⋮ On number and evenness of solutions of the \(SU(3)\) Toda system on flat tori with non-critical parameters ⋮ On the asymptotics for minimizers of Donaldson functional in Teichmüller theory ⋮ Estimates of Bubbling Solutions of $SU(3)$ Toda Systems at Critical Parameters. Part 1 ⋮ Existence results for Liouville equations and systems ⋮ The blow-up analysis of an affine Toda system corresponding to superconformal minimal surfaces in \(\mathbb{S}^4\) ⋮ Analytic aspects of the Tzitzéica equation: blow-up analysis and existence results ⋮ 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 ⋮ Degree counting theorems for singular Liouville systems ⋮ Even solutions of some mean field equations at non-critical parameters on a flat torus

Cites Work

• Unnamed Item
• Unnamed Item
• On Liouville systems at critical parameters. I: One bubble
• Mean field equations, hyperelliptic curves and modular forms. I
• Profile of bubbling solutions to a Liouville system
• Harnack type inequality: The method of moving planes
• Asymptotic radial symmetry for solutions of \(\Delta u+e^ u=0\) in a punctured disc
• The relativistic non-Abelian Chern-Simons equations
• When ``blow-up does not imply ``concentration: a detour from Brézis-Merle's result
• Classification and nondegeneracy of \(SU(n+1)\) Toda system with singular sources
• The Liouville equation with singular data: a concentration-compactness principle via a local representation formula.
• Existence of bubbling solutions for Chern-Simons model on a torus
• Classification of blowup limits for \(\mathrm{SU}(3)\) singular Toda systems
• New blow-up phenomena for \(\mathrm{SU}(n+1)\) Toda system
• On a class of elliptic problems in R²: symmetry and uniqueness results
• Prescribing Curvature on Compact Surfaces with Conical Singularities
• Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)e^uin two dimensions
• Self-dual non-Abelian Chern-Simons solitons
• Energy Concentration and A Priori Estimates forB₂andG₂Types of Toda Systems

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