  In 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.
