Hölder continuity for second order elliptic problems with nonsmooth data
Robert Haller‐Dintelmann, Christian Meyer, Joachim Rehberg · 2008
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.