  The purpose of this paper is to prove local upper and lower bounds for weak
solutions of semilinear elliptic equations of the form $-\Delta u= c u^p$, with
$0<p<p_s=(d+2)/(d-2)$, defined on bounded domains of $\RR^d$, $d\ge 3$, without
reference to the boundary behaviour. We give an explicit expression for all the
involved constants. As a consequence, we obtain local Harnack inequalities with
explicit constant, as well as gradient bounds.
