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 |
| _version_ | 1798043372468830208 |
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| author | Jerico B. Bacani Gunther Peichl |
| author_facet | Jerico B. Bacani Gunther Peichl |
| author_sort | Jerico B. Bacani |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T22:48:09Z |
| format | Article |
| id | doaj.art-8292f8b317054e6ca2d867dcc73caa21 |
| institution | Directory Open Access Journal |
| issn | 1085-3375 1687-0409 |
| language | English |
| last_indexed | 2024-04-11T22:48:09Z |
| publishDate | 2013-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj.art-8292f8b317054e6ca2d867dcc73caa212022-12-22T03:58:41ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/384320384320On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli ProblemJerico B. Bacani0Gunther Peichl1Department of Mathematics and Computer Science, University of the Philippines Baguio, Governor Pack Road, Baguio City 2600, PhilippinesInstitute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, A-8010 Graz, AustriaThe 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.http://dx.doi.org/10.1155/2013/384320 |
| spellingShingle | Jerico B. Bacani Gunther Peichl On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli Problem Abstract and Applied Analysis |
| title | On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli Problem |
| title_full | On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli Problem |
| title_fullStr | On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli Problem |
| title_full_unstemmed | On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli Problem |
| title_short | On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli Problem |
| title_sort | on the first order shape derivative of the kohn vogelius cost functional of the bernoulli problem |
| url | http://dx.doi.org/10.1155/2013/384320 |
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