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Optimization problems for weighted Sobolev constants

Bandle, Catherine ; Wagner, Alfred

In: Calculus of Variations and Partial Differential Equations, 2007, vol. 29, no. 4, p. 481-507

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    Title
    • Optimization problems for weighted Sobolev constants
    Author
    • Bandle, Catherine. Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051, Basel, Switzerland
    • Wagner, Alfred. Institut für Mathematik, RWTH Aachen, Templergraben 55, 52062, Aachen, Germany
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Calculus of Variations and Partial Differential Equations, 2007, vol. 29, no. 4, p. 481-507. Springer-Verlag
    Other Version
    Classification
    • Mathematics
    OAI-PMH Identifier
    • oai:doc.rero.ch:319282
    Summary
    In this paper, we study a variational problem under a constraint on the mass. Using a penalty method we prove the existence of an optimal shape. It will be shown that the minimizers are Hölder continuous and that for a large class they are even Lipschitz continuous. Necessary conditions in form of a variational inequality in the interior of the optimal domain and a condition on the free boundary are derived