On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli Problem
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 solvin...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/384320 |
| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |