The blow-up analysis of an affine Toda system corresponding to superconformal minimal surfaces in \(\mathbb{S}^4\)

DOI10.1016/j.jfa.2021.109194zbMath1473.35069arXiv2011.01425OpenAlexW3185290544MaRDI QIDQ1982523

Lei Liu, Guofang Wang

Publication date: 14 September 2021

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.01425

zbMATH Keywords

Liouville equationglobal Pohozaev identityopen and affine Toda system

Mathematics Subject Classification ID

Semilinear elliptic equations (35J61) Second-order elliptic systems (35J47) Blow-up in context of PDEs (35B44) PDEs on manifolds (35R01)

Related Items

Exact solutions for two dimensional \(D_n^{(1)}\) Toda equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analytic aspects of the Tzitzéica equation: blow-up analysis and existence results
• Holomorphic curves and Toda systems
• The scalar-curvature problem on the standard three-dimensional sphere
• Harmonic maps from surfaces to complex projective spaces
• Topological methods for an elliptic equation with exponential nonlinearities
• Non-simple blow-up solutions for the Neumann two-dimensional sinh-Gordon equation
• Nonuniqueness in the Plateau problem for surfaces of constant mean curvature
• Prescribing Gaussian curvature on S 2
• On conformal minimal immersions of \(S^ 2\) into \({\mathbb{C}}P^ n\)
• Representation theory and integration of nonlinear spherically symmetric equations to gauge theories
• Integrable nonlinear Klein-Gordon equations and Toda lattices
• The existence of minimal immersions of 2-spheres
• Classification of solutions of some nonlinear elliptic equations
• Estimate of the conformal scalar curvature equation via the method of moving planes. II
• Harnack type inequality: The method of moving planes
• Existence results for mean field equations
• The scalar curvature equation on 2- and 3-spheres
• On rank-2 Toda systems with arbitrary singularities: local mass and new estimates
• Classification and nondegeneracy of \(SU(n+1)\) Toda system with singular sources
• Classification of blow-up limits for the sinh-Gordon equation.
• What kinds of singular surfaces can admit constant curvature?
• Energy identity for a class of approximate harmonic maps from surfaces
• A priori estimates for \(D_4\) and \(F_4\) Toda systems
• \textit{A priori} estimates of Toda systems. I: The Lie algebras of \(\mathbf{A}_n, \mathbf{B}_n, \mathbf{C}_n\) and \(\mathbf{G}_2\)
• Classification of blowup limits for \(\mathrm{SU}(3)\) singular Toda systems
• Multiple blow-up phenomena for the sinh-Poisson equation
• The blow up analysis of solutions of the elliptic sinh-Gordon equation
• Multiple solutions ofH-systems and Rellich's conjecture
• Scalar Curvatures on S 2
• Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)e^uin two dimensions
• Analytic aspects of the Toda system: I. A Moser‐Trudinger inequality
• Self-Dual Chern-Simons Theories
• On the topological degree of the mean field equation with two parameters
• Analytic aspects of the Toda system: II. Bubbling behavior and existence of solutions