Applied Mathematics and Optimization

, Volume 60, Issue 3, pp 397–428 | Cite as

Hölder Continuity and Optimal Control for Nonsmooth Elliptic Problems

  • R. Haller-Dintelmann
  • C. Meyer
  • J. Rehberg
  • A. Schiela
Article
First Online:
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Accepted:

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.

Keywords

Elliptic problems Mixed boundary value problems Hölder continuity Optimal control 
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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • R. Haller-Dintelmann
    • 1
  • C. Meyer
    • 2
  • J. Rehberg
    • 2
  • A. Schiela
    • 3
  1. 1.Technische Universität DarmstadtDarmstadtGermany
  2. 2.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany
  3. 3.Konrad-Zuse-Zentrum für Informationstechnik BerlinBerlinGermany

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