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On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli Problem

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  • Jerico B. Bacani
  • Gunther Peichl

Abstract

The exterior Bernoulli free boundary problem is being considered. The solution to the problem is studied via shape optimization techniques. The goal is to determine a domain having a specific regularity that gives a minimum value for the Kohn-Vogelius-type cost functional while simultaneously solving two PDE constraints: a pure Dirichlet boundary value problem and a Neumann boundary value problem. This paper focuses on the rigorous computation of the first-order shape derivative of the cost functional using the Hölder continuity of the state variables and not the usual approach which uses the shape derivatives of states.

Suggested Citation

  • Jerico B. Bacani & Gunther Peichl, 2013. "On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli Problem," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-19, December.
    • Handle: RePEc:hin:jnlaaa:384320
    DOI: 10.1155/2013/384320
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    Cited by:

    1. Jerico B. Bacani & Gunther Peichl, 2014. "The Second-Order Shape Derivative of Kohn–Vogelius-Type Cost Functional Using the Boundary Differentiation Approach," Mathematics, MDPI, vol. 2(4), pages 1-22, September.

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