Precise blowup rate near the boundary of boundary blowup solutions to k-Hessian equation

We consider boundary blowup problem for k-Hessian equation of the form $$F_k[u] = f(x)g(u)$$ F k [ u ] = f ( x ) g ( u ) in a uniformly $$(k-1)$$ ( k - 1 ) -convex domain $$\Omega \subset {\mathbb {R}}^n$$ Ω ⊂ R n , where f(x) behaves like $$\mathop {\mathrm {dist}} \nolimits (x,\partial \Omega )^{\alpha }$$ dist ( x , ∂ Ω ) α as $$\text {dist}(x,\partial \Omega ) \rightarrow 0$$ dist ( x , ∂ Ω ) → 0 and g(u) behaves like $$u^p$$ u p as $$u \rightarrow \infty$$ u → ∞ . We obtain the precise blowup rate of a solution u near the boundary $$\partial \Omega$$ ∂ Ω .