The purpose of this paper is to prove local upper and lower bounds for weak solutions of semilinear elliptic equations of the form −Δu = cup, with 0 < p < ps = (d + 2)/(d - 2), defined on bounded domains of \documentclass[12pt]{minimal}
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\begin{document}$${{\mathbb{R}^d}, d \geq 3}$$\end{document}, 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 constants, as well as gradient bounds.
