The C0-convergence at the Neumann boundary for Liouville equations

作者：Bi, Yuchen; Li, Jiayu; Liu, Lei^*; Peng, Shuangjie

来源：Calculus of Variations and Partial Differential Equations, 2023, 62(3): 107.

DOI：10.1007/s00526-023-02447-0

• 35J60
• 35J57
• 35B44

In this paper, we study the blow-up analysis for a sequence of solutions to the Liouville type equation with exponential Neumann boundary condition. For interior case, i.e. the blow-up point is an interior point, Li (Commun Math Phys 200(2):421-444, 1999) gave a uniform asymptotic estimate. Later, Zhang (Commun Math Phys 268(1):105-133, 2006) and Gluck (Nonlinear Anal 75(15):5787-5796, 2012) improved Li's estimate in the sense of C0-convergence by using the method of moving planes or classification of solutions of the linearized version of Liouville equation. If the sequence blows up at a boundary point, Bao- Wang-Zhou (J Math Anal Appl 418:142-162, 2014) proved a similar asymptotic estimate of Li (1999). In this paper, we will prove a C0-convergence result in this boundary blow-up process. Our method is different from Gluck (2013), Zhang (2006).

• 单位
  中国科学院研究生院