We present an explicit pluripotential and viscosity solution to the complex Monge–Ampère equation with constant right-hand side on \({\mathbb {D}}\times {\mathbb {C}}^{n-1}\) \((n\ge 2)\) , which lies merely in \(W^{1,2}_{{\textrm{loc}}}\cap W^{2,1}_{{\textrm{loc}}}\) and is not even Dini continuous. Additionally, we exhibit two families of explicit entire toric solutions on \(\mathbb C^n\) \((n\ge 2)\) with continuous Hölder exponent \(\alpha \in (0,1)\) and \(W^{2,p}_{{\textrm{loc}}}\) exponent \(p\in (1,2)\) .
