Higher order boundary estimates for blow-up solutions of elliptic equations

Abstract

We investigate blow-up solutions of the equation $\Delta u=u^p+g(u)$ in a bounded smooth domain $\Omega$. If $p>1$ and if $g$ satisfies appropriate growth conditions (compared with the growth of $t^p$) as $t$ goes to infinity we find optimal asymptotic estimates of the solution $u(x)$ in terms of the distance of $x$ from the boundary $\partial\Omega$.