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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.

Document Type: Research Article

Affiliations: 1: Institut für Mathematik, Universität Würzburg, 97074 Würzburg, Germany 2: Technische Universität Chemnitz, Faculty of Mathematics, 09107 Chemnitz, Germany

Publication date: January 1, 2014

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