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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 384320, 19 pages
Research Article

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

1Department of Mathematics and Computer Science, University of the Philippines Baguio, Governor Pack Road, Baguio City 2600, Philippines
2Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, A-8010 Graz, Austria

Received 18 August 2013; Accepted 1 November 2013

Academic Editor: Sergei V. Pereverzyev

Copyright © 2013 Jerico B. Bacani and Gunther Peichl. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.