Dependence of blowup rate of large solutions of semilinear elliptic equations, on the curvature of the boundary.

Let D be a smooth bounded domain in . Let f be a positive monotone increasing function on which satisfies the Keller-Osserman condition. It is well-known that the solutions of Δ u = f ( u ), which blow up at the boundary behave, to a first order approximation, like a function of dist( x ,∂ D ). In this paper we show that the second order approximation depends on the mean curvature of ∂ D . This paper is an extension of results in [4] which dealt with radially symmetric solutions. It extends also the results in [5] for f = t p . [ABSTRACT FROM AUTHOR]