Analysis & PDE

  • Anal. PDE
  • Volume 11, Number 4 (2018), 873-898.

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

Chang-Shou Lin, Jun-cheng Wei, Wen Yang, and Lei Zhang

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Abstract

For all rank-2 Toda systems with an arbitrary singular source, we use a unified approach to prove:

  1. The pair of local masses ( σ 1 , σ 2 ) at each blowup point has the expression σ i = 2 ( N i 1 μ 1 + N i 2 μ 2 + N i 3 ) , where N i j , i = 1 , 2 , j = 1 , 2 , 3 .
  2. At each vortex point p t if ( α t 1 , α t 2 ) are integers and ρ i 4 π , then all the solutions of Toda systems are uniformly bounded.
  3. If the blowup point q is a vortex point p t and α t 1 , α t 2 and 1 are linearly independent over Q , then u k ( x ) + 2 log | x p t | C .

The Harnack-type inequalities of 3 are important for studying the bubbling behavior near each blowup point.

Article information

Source
Anal. PDE, Volume 11, Number 4 (2018), 873-898.

Dates
Received: 3 November 2016
Revised: 17 August 2017
Accepted: 5 December 2017
First available in Project Euclid: 1 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.apde/1517454157

Digital Object Identifier
doi:10.2140/apde.2018.11.873

Mathematical Reviews number (MathSciNet)
MR3749370

Zentralblatt MATH identifier
1383.35078

Subjects
Primary: 35J47: Second-order elliptic systems
Secondary: 35J60: Nonlinear elliptic equations 35J55

Keywords
SU$(n{+}1)$-Toda system asymptotic analysis a priori estimate classification theorem topological degree blowup solutions Riemann–Hurwitz theorem

Citation

Lin, Chang-Shou; Wei, Jun-cheng; Yang, Wen; Zhang, Lei. On rank-2 Toda systems with arbitrary singularities: local mass and new estimates. Anal. PDE 11 (2018), no. 4, 873--898. doi:10.2140/apde.2018.11.873. https://projecteuclid.org/euclid.apde/1517454157


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