2017/07/08 by Man Chun Leung, Leung, Man Chun
Computer Science · Mathematics · #35J60 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP #msc:35J60
paper · pdf · doi:10.48550/arxiv.1707.02401
Contain an e-Appendix (page 44 onward)
arxiv created 2017/07/08 · openalex publication_date 2017/07/08 · arxiv updated 2017/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In their work on a sharp compactness theorem for the Yamabe problem, Khuri, Marques and Schoen apply a refined blow-up analysis (what we call `second order blow-up argument' in this article) to obtain highly accurate approximate solutions for the Yamabe equation. As for the conformal scalar curvature equation on Sn with n > 3, we examine the second order blow-up argument and obtain refined estimate for a blow-up sequence near a simple blow-up point. The estimate involves local effect from the Taylor expansion of the scalar curvature function, global effect from other blow-up points, and the balance formula as expressed in the Pohozaev identity in an essential way.