Abstract
We study an optimal design problem for the domain of an elliptic equation with Dirichlet boundary conditions. We introduce a relaxed formulation of the problem which always admits a solution, and we prove some necessary conditions for optimality both for the relaxed and for the original problem.
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Buttazzo, G., Dal Maso, G. Shape optimization for Dirichlet problems: Relaxed formulation and optimality conditions. Appl Math Optim 23, 17–49 (1991). https://doi.org/10.1007/BF01442391
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DOI: https://doi.org/10.1007/BF01442391