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

Abstract

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 = tp .