Optimal uniqueness theorems and exact blow-up rates of large solutions

In this paper, we prove some optimal uniqueness results for large solutions of a canonical class of semilinear equations under minimal regularity conditions on the weight function in front of the non-linearity and combine these results with the localization method introduced in [López-Gómez, The boundary blow-up rate of large solutions, J. Differential Equations 195 (2003) 25–45] to prove that any large solution of Δu=a(x)up, p>1, a>0, must satisfy where and fx0 is any smooth extension of the boundary normal section of a at x0 ∂Ω, i.e., Subsequently, nx0 stands for the outward unit normal at x0 ∂Ω. Therefore, the theory can be extended to cover the general case when .