Some complementary estimates in the Dead Core problem

Abstract

This article is concerned with some estimates in the problem $\Delta u = c^2 u^p$ in $\Omega$, $u = 1$ on $\partial \Omega$. The quantities of interest here are the critical value of $c$ for which a dead core $\Omega_0$ exists, the location of $\Omega_0$ and the effectiveness factor.