Estimates of bubbling solutions of SU(3) Toda systems at critical parameters-Part 1

2019/12/27 by Wu, Lina, Zhang, Lei
#35J47 #58J05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.12071

Abstract

For regular SU(3) Toda systems defined on Riemann surface, we initiate the study of bubbling solutions if parameters (ρ₁^k,ρ₂^k) are both tending to critical positions: (ρ₁^k,ρ₂^k)→ (4π, 4πN) or (4πN, 4π) (N>0 is an integer). We prove that there are at most three formations of bubbling profiles, and for each formation we identify leading terms of ρ₁^k-4π and ρ₂^k-4πN, locations of blowup points and comparison of bubbling heights with sharp precision. The results of this article will be used as substantial tools for a number of degree counting theorems, critical point at infinity theory in the future.

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