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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- 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