Interfaces and Free Boundaries

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Volume 11, Issue 2, 2009, pp. 317–330
DOI: 10.4171/IFB/213

Published online: 2009-06-30

On the shape derivative for problems of Bernoulli type

J. Haslinger[1], K. Ito[2], T. Kozubek[3], Karl Kunisch[4] and G. Peichl[5]

(1) Charles University, Praha, Czech Republic
(2) North Carolina State University, Raleigh, United States
(3) VSB-Technical University Ostrava, Czech Republic
(4) Karl-Franzens-Universit├Ąt Graz, Austria
(5) Karl-Franzens-Universit├Ąt Graz, Austria

The shape derivative of the cost functional in a Bernoulli-type problem is characterized. The calculation of the derivative of the cost does not use the shape derivative of the state variable and is achieved under mild regularity conditions on the boundary of the domain.

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Haslinger J., Ito K., Kozubek T., Kunisch Karl, Peichl G.: On the shape derivative for problems of Bernoulli type. Interfaces Free Bound. 11 (2009), 317-330. doi: 10.4171/IFB/213