  Given a smooth domain $\Omega\subset\RR^N$ such that $0 \in \partial\Omega$
and given a nonnegative smooth function $\zeta$ on $\partial\Omega$, we study
the behavior near 0 of positive solutions of $-\Delta u=u^q$ in $\Omega$ such
that $u = \zeta$ on $\partial\Omega\setminus\{0\}$. We prove that if
$\frac{N+1}{N-1} < q < \frac{N+2}{N-2}$, then $u(x)\leq C
\abs{x}^{-\frac{2}{q-1}}$ and we compute the limit of $\abs{x}^{\frac{2}{q-1}}
u(x)$ as $x \to 0$. We also investigate the case $q= \frac{N+1}{N-1}$. The
proofs rely on the existence and uniqueness of solutions of related equations
on spherical domains.
