Optimality conditions for the continuous model of the final open pit problem (Q828728)

The authors discuss optimality conditions for the ``final open pit problem''. Here they model a pit as a depth function \(p\) over some domain \(\Omega \subset \mathbb{R}^d\), to be determined, maximizing the gain obtained from excavating the pit. For with additional constraints on the function values of \(p\), its slope, and a bound on the associated costs of the excavation. For this problem, the authors derive optimality conditions for the case \(d = 1\) and \(d =2\). In the case \(d=2\), the authors only provide conditions on subdomains \(\Omega_0 \subset \Omega\) on which the slope constraints remain inactive.