On the solutions of the equation Delta u=e(u) blowing up on the boundary

Let Omega be an open bounded set of R(n); we consider the equation Delta u = e(u) in Omega with the boundary condition lim(x-partial derivative Omega) u(x) = +infinity. We prove estimates for the solution u(x) and for the measure of Omega comparing this problem with a problem of the same type defined in a ball. If n = 2 we obtain an explicit estimate of the minimum of u(x) in terms of the measure of Omega.