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search.filters.applied.f.access: openAccess × Author: Meyer, Christian × Author: Rehberg, Joachim × End date: 2009 × Start date: 2000 × DDC: 510 × Type: Text × Version: publishedVersion ×

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    Optimal control for the thermistor problem
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Hömberg, Dietmar; Meyer, Christian; Rehberg, Joachim; Ring, Wolfgang
    This paper is concerned with the state-constrained optimal control of the two-dimensional thermistor problem, a quasi-linear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Existence, uniqueness and continuity for the state system are derived by employing maximal elliptic and parabolic regularity. By similar arguments the linearized state system is discussed, while the adjoint system involving measures is investigated using a duality argument. These results allow to derive first-order necessary conditions for the optimal control problem.
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    Hölder continuity for second order elliptic problems with nonsmooth data
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Haller-Dintelmann, Robert; Meyer, Christian; Rehberg, Joachim
    The well known De Giorgi result on Hölder continuity for solutions of the Dirichlet problem is re-established for mixed boundary value problems, provided that the underlying domain is a Lipschitz domain and the border between the Dirichlet and the Neumann boundary part satisfies a very general geometric condition. Implications of this result for optimal control theory are presented.