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Open AccessArticle

The Second-Order Shape Derivative of Kohn–Vogelius-Type Cost Functional Using the Boundary Differentiation Approach

1
Department of Mathematics and Computer Science, College of Science, University of the Philippines Baguio, Governor Pack Road, Baguio 2600, Philippines
2
Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, A-8010 Graz, Austria
*
Author to whom correspondence should be addressed.
Mathematics 2014, 2(4), 196-217; https://doi.org/10.3390/math2040196
Received: 31 December 2013 / Revised: 26 August 2014 / Accepted: 1 September 2014 / Published: 26 September 2014
(This article belongs to the Special Issue Mathematics on Partial Differential Equations)
A shape optimization method is used to study the exterior Bernoulli free boundaryproblem. We minimize the Kohn–Vogelius-type cost functional over a class of admissibledomains subject to two boundary value problems. The first-order shape derivative of the costfunctional is recalled and its second-order shape derivative for general domains is computedvia the boundary differentiation scheme. Additionally, the second-order shape derivative ofJ at the solution of the Bernoulli problem is computed using Tiihonen’s approach. View Full-Text
Keywords: Bernoulli problem; boundary value problems; shape derivative; boundary differentiation Bernoulli problem; boundary value problems; shape derivative; boundary differentiation
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Bacani, J.B.; Peichl, G. The Second-Order Shape Derivative of Kohn–Vogelius-Type Cost Functional Using the Boundary Differentiation Approach. Mathematics 2014, 2, 196-217.

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