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Title: On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli Problem
Authors: Bacani, Jerico B.
Peichl, Gunther
Issue Date: 1-Nov-2013
Publisher: Hindawi Publishing Corporation
Citation: Abstract and Applied Analysis, Volume 2013, Article ID 384320, 19 pages
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 H¨older continuity of the state variables and not the usual approach which uses the shape derivatives of states.
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