2009•Interfaces and Free Boundaries Mathematical Analysis Computation and ApplicationsOpen access

On the shape derivative for problems of Bernoulli type

Jaroslav Haslinger, Kazufumi Ito, Tomáš Kozubek, Karl Kunisch, G. Peichl

Abstract

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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Key concepts: Bernoulli's principle, Derivative (finance), Material derivative, Domain (mathematical analysis), Generalizations of the derivative, Type (biology), Boundary (topology), Second derivative