Interfaces and Free Boundaries


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

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) Department of Numerical Analysis, Charles University, Sokolovska 83, 180 00, PRAHA 8-KARLIN, CZECH REPUBLIC
(2) Department of Mathematics, North Carolina State University, Campus Box 8205, NC 27695-8205, RALEIGH, UNITED STATES
(3) Department of Applied Mathematics, VSB-Technical University Ostrava, 17. listopadu 15, 708 33, OSTRAVA-PORUBA, CZECH REPUBLIC
(4) Institut für Mathematik, Karl-Franzens-Universität Graz, Heinrichstr. 36, 8010, GRAZ, AUSTRIA
(5) Institut für Mathematik, Karl-Franzens-Universität Graz, Heinrichstr. 36, 8010, 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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