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

Abstract

We consider boundary blowup problem for k-Hessian equation of the form F k ½u ¼ f ðxÞgðuÞ in a uniformly ðk À 1Þ-convex domain X & R n , where f(x) behaves like distðx; oXÞ a as distðx; oXÞ ! 0 and g(u) behaves like u p as u ! 1. We obtain the precise blowup rate of a solution u near the boundary oX.