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Hölder Continuity and Optimal Control for Nonsmooth Elliptic Problems

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Abstract

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.

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Authors and Affiliations

  1. Technische Universität Darmstadt, Schlossgartenstr. 7, 64289, Darmstadt, Germany

    R. Haller-Dintelmann

  2. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117, Berlin, Germany

    C. Meyer & J. Rehberg

  3. Konrad-Zuse-Zentrum für Informationstechnik Berlin, Takustr. 7, 14195, Berlin, Germany

    A. Schiela

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  1. R. Haller-Dintelmann
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  2. C. Meyer
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  3. J. Rehberg
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  4. A. Schiela
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Correspondence to C. Meyer.

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Haller-Dintelmann, R., Meyer, C., Rehberg, J. et al. Hölder Continuity and Optimal Control for Nonsmooth Elliptic Problems. Appl Math Optim 60, 397–428 (2009). https://doi.org/10.1007/s00245-009-9077-x

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  • DOI: https://doi.org/10.1007/s00245-009-9077-x

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