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Tracking Dirichlet Data in L 2 is an Ill-Posed Problem

Author

Listed:
  • K. Eppler

    (Technische Universität Dresden)

  • H. Harbrecht

    (Universität Bonn)

Abstract

A stationary free boundary problem is solved by tracking the Dirichlet data at the free boundary. The shape gradient and Hessian of the tracking functional under consideration are computed. By analyzing the shape Hessian in case of matching Dirichlet data, it is shown that this shape optimization problem is algebraically ill-posed. Numerical experiments are carried out to validate and quantify the results.

Suggested Citation

  • K. Eppler & H. Harbrecht, 2010. "Tracking Dirichlet Data in L 2 is an Ill-Posed Problem," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 17-35, April.
    • Handle: RePEc:spr:joptap:v:145:y:2010:i:1:d:10.1007_s10957-009-9630-4
    DOI: 10.1007/s10957-009-9630-4
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    Cited by:

    1. Karsten Eppler & Helmut Harbrecht, 2012. "On a Kohn-Vogelius like formulation of free boundary problems," Computational Optimization and Applications, Springer, vol. 52(1), pages 69-85, May.
    2. A. Boulkhemair & A. Chakib & A. Nachaoui & A. A. Niftiyev & A. Sadik, 2020. "On a numerical shape optimization approach for a class of free boundary problems," Computational Optimization and Applications, Springer, vol. 77(2), pages 509-537, November.
    3. Julius Fergy T. Rabago & Hideyuki Azegami, 2020. "A second-order shape optimization algorithm for solving the exterior Bernoulli free boundary problem using a new boundary cost functional," Computational Optimization and Applications, Springer, vol. 77(1), pages 251-305, September.

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