Estimates for Boundary Blowup Solutions of p-Laplacian Type Quasilinear Elliptic Equations

In this paper, we investigate the effect of the mean curvature of the boundary ∂Ω on the behavior of the blow-up solutions to the p-Laplacian type quasilinear elliptic equation

div(|∇u|p-2∇u) = um|∇u|, p > 1,

where the Ω ∈ RN be a bounded smooth domain. Under appropriate conditions on p and m, we find the estimates of the solution u interms of the distance from x to the boundary ∂Ω. To the equation

div(|∇u|p-2∇u) = um|∇u|q, p > 1, 0 < q < 1,

the results of the semilinear problem are extended to the quasilinear ones.