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In this paper the quaternary continuous classical optimal control problem (QCCOCP) for the quaternary linear elliptic partial differential equations (QLEPDEqs). The existence of a unique state vector solution (QSVS) of the weak form (WF) for the QLEPDEqs is stated and proved for fixed quaternary classical continuous control vector (QCCCV) using the method of Galekin (MG) . Furthermore, the existence of quaternary classical continuous optimal control vector (QCCOCV) ruled by the QLEPDEqs is stated and proved. The quaternary adjoint equations (QAJEqs) associated with the QLEPDEqs is studied. The Fréchet derivative (FD) for the objective function (OF) is derived. Finally, the necessary condition theorem (NCTH) for the optimality is proved. more...