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Mathematics 2014, 2(4), 196-217; doi:10.3390/math2040196

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.
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)
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Abstract

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
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. (CC BY 4.0).

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MDPI and ACS Style

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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