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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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