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.
Cite this article
Karl Kunisch, J. Haslinger, K. Ito, T. Kozubek, G. Peichl, On the shape derivative for problems of Bernoulli type. Interfaces Free Bound. 11 (2009), no. 2, pp. 317–330DOI 10.4171/IFB/213