2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226087In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The control is applied to the state equation via the boundary and a functional of the control together with the solution of the state equation under such a control will be minimized. A constrain on the solution of the state equation is also considered.15 pagesAnalysis of PDEsOptimization and Control49K20; 49B22; 35J25text