On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli Problem

Bacani, Jerico B.; Peichl, Gunther

dc.contributor.author	Bacani, Jerico B.
dc.contributor.author	Peichl, Gunther
dc.date.accessioned	2019-09-16T03:46:31Z
dc.date.available	2019-09-16T03:46:31Z
dc.date.issued	2013-11-01
dc.identifier.citation	Abstract and Applied Analysis, Volume 2013, Article ID 384320, 19 pages	en_US
dc.identifier.uri	http://dx.doi.org/10.1155/2013/384320
dc.identifier.uri	http://dspace.upb.edu.ph/jspui/handle/123456789/35
dc.description.abstract	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 H¨older continuity of the state variables and not the usual approach which uses the shape derivatives of states.	en_US
dc.description.sponsorship	The paper is partially supported by the ¨OAD—Austrian Agency for International Cooperation in Education and Research for the Technologiestipendien S¨udostasien (Doktorat) scholarship in the frame of the ASEA-Uninet; the SFB Research Center “Mathematical Optimization and Applications in Biomedical Sciences” SFB F32; the University of the Philippines Baguio.The first author is thankful to the Institute for Mathematics and Scientific Computing, University of Graz, for funding a presentation of partial results during the 7th European Conference on Elliptic and Parabolic Problems held on May 21–25, 2012 at Gaeta, Italy. He is likewise grateful to Professor Gilbert Peralta for his helpful insights and suggestions. Moreover, he is thanking UP Baguio for giving a Ph.D. incentive grant for writing this paper. Last but not least, the authors would like to thank the referees for devoting time to review this material.	en_US
dc.language.iso	en	en_US
dc.publisher	Hindawi Publishing Corporation	en_US
dc.title	On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli Problem	en_US
dc.type	Article	en_US