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Title: The Second-Order Shape Derivative of Kohn–Vogelius-Type Cost Functional Using the Boundary Differentiation Approach
Authors: Bacani, Jerico B.
Peichl, Gunther
Keywords: Bernoulli problem
boundary value problems
shape derivative
boundary differentiation
Issue Date: 26-Sep-2014
Citation: Mathematics 2014, 12, 196-217
Abstract: A shape optimization method is used to study the exterior Bernoulli free boundary problem. We minimize the Kohn–Vogelius-type cost functional over a class of admissible domains subject to two boundary value problems. The first-order shape derivative of the cost functional is recalled and its second-order shape derivative for general domains is computed via the boundary differentiation scheme. Additionally, the second-order shape derivative of J at the solution of the Bernoulli problem is computed using Tiihonen’s approach.
URI: doi:10.3390/math2040196
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