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The Existence of Optimal Solution for a Shape Optimization Problem on Starlike Domain

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Abstract

In this paper, a shape optimization problem over a multi-dimensional starlike domain with boundary payoff is considered. The function, which characterizes the boundary of the domain with respect to some ball contained inside domain, is shown to be Lipschitz continuous. The existence of an optimal solution is proved.

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Authors and Affiliations

  1. School of Mathematics, Central South University, Changsha, 410075, China

    Y. He

  2. Academy of Mathematics and Systems Science, Academia Sinica, Beijing, 100190, China

    B. Z. Guo

  3. School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, China

    B. Z. Guo

  4. School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa

    B. Z. Guo

Authors
  1. Y. He
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  2. B. Z. Guo
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Correspondence to B. Z. Guo.

Additional information

Communicated by Qianchuan Zhao.

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He, Y., Guo, B.Z. The Existence of Optimal Solution for a Shape Optimization Problem on Starlike Domain. J Optim Theory Appl 152, 21–30 (2012). https://doi.org/10.1007/s10957-011-9878-3

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  • DOI: https://doi.org/10.1007/s10957-011-9878-3

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