OPTIMAL CONTROL OF AN OBLIQUE DERIVATIVE PROBLEM

We investigate optimal control of an elliptic partial differential equation (PDE) with oblique b oundary conditions. These b oundary conditions do not lead directly to a weak formulation of the PDE. Thus, the equation is reformulated as a variational problem. Existence of optimal controls and regularity of solutions is proven. First-order optimality conditions are investigated. The adjoint state is interpreted as the solution of a b oundary value problem with non-variational boundary conditions. Numerical results demonstrate the approximative solution of the optimal control problem by finite element discretization.