WIAS Preprint No. 1316, (2008)

Hölder continuity for second order elliptic problems with nonsmooth data


  • Haller-Dintelmann, Robert
  • Meyer, Christian
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 35B65 35J25 35R05 49K20


  • Elliptic problems, mixed boundary value problems, Hölder continuity, optimal control


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.

Appeared in

  • Appl. Math. Optim., 60 (2009) pp. 397--428.

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