be a bounded smooth domain in
. It is well known that large solutions of an equation such as
blow up at the boundary at a rate
which depends only on
denotes the distance of
to the boundary.) In this paper the authors consider a secondary effect in the asymptotic behaviour of solutions, namely, the behaviour of
. They derive estimates for this expression, which are valid for a large class of nonlinearities and extend a recent result of Lazer and McKenna.