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