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Optimal shape design for systems governed by variational inequalities, part 1: Existence theory for the elliptic case

Abstract

Some general existence results for optimal shape design problems for systems governed by elliptic variational inequalities are established by the mapping method and variational convergence theory. Then, an existence theorem is given for the optimal shape for an electrochemical machining problem, in which the cost functional is not lower semicontinuous, by extending the general results to this case. Furthermore, this problem is approximated by a set of optimal shape design problems which have more smooth cost functionals and are easier to handle computationally.

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The authors with to express their sincere thanks to the reviewers for supplying additional references and for their valuable comments, which made the paper more readable.

Communicated by E. J. Haug

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Liu, W.B., Rubio, J.E. Optimal shape design for systems governed by variational inequalities, part 1: Existence theory for the elliptic case. J Optim Theory Appl 69, 351–371 (1991). https://doi.org/10.1007/BF00940649

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Key Words

  • Optimal shape design
  • variational convergence theory
  • elliptic variational inequalities
  • existence theorems