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
$$C^0$$
-convergence by using the method of moving planes or classification of solutions of the linea...
