Authors’ abstract: We study the second order estimate for the unique solution near the boundary to the singular Dirichlet problem \(-\Delta u=b(x)g(u)\), \(u>0\), \(x\in\Omega\), \(u| _{\partial\Omega}=0\), where \(\Omega\) is a bounded domain with smooth boundary in \(\mathbb R^N\), \(g\in C^1((0,\infty),(0,\infty))\), \(g\) is decreasing on \((0,\infty)\) with \(\lim_{s\to0^+}g(s)=\infty\) and \(g\) is normalized regularly varying at zero with index \(-\gamma\) (\(\gamma>1\)), \(b\in C^\alpha(\bar\Omega)\) (\(0<\alpha<1\)), is positive in \(\Omega\), may be vanishing on the boundary. Our analysis is based on Karamata regular variation theory.