Optimal boundary expansions of the solution to an elliptic problem with a singular nonlinearity

This paper investigates the boundary behavior of solutions to a singular Dirichlet problem: − Δ u = d ( x ) α u − p , u > 0 , x ∈ Ω , u | ∂ Ω = 0 , where Ω ⊂ R n is smooth bounded domain, d ( x ) = dist ( x , ∂ Ω ) denotes the boundary distance function. We establish asymptotic expansion in a small neighborhood of the boundary and this expansion formula shows the singularity profile of solutions at the boundary.