Geodesic
Shape Hessian for generalized Oseen flow by differentiability of a minimax: A Lagrangian approach
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 987-1011.

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The goal of this paper is to compute the shape Hessian for a generalized Oseen problem with nonhomogeneous Dirichlet boundary condition by the velocity method. The incompressibility will be treated by penalty approach. The structure of the shape gradient and shape Hessian with respect to the shape of the variable domain for a given cost functional are established by an application of the Lagrangian method with function space embedding technique.
Classification : 49K35, 49Q12, 76D07, 76D55
Keywords: shape sensitivity analysis; shape Hessian; Eulerian semiderivative; differentiability of a minimax; Oseen flow 
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     author = {Gao, Zhiming and Ma, Yichen and Zhuang, Hongwei},
     title = {Shape {Hessian} for generalized {Oseen} flow by differentiability of a minimax: {A} {Lagrangian} approach},
     journal = {Czechoslovak Mathematical Journal},
     pages = {987--1011},
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     volume = {57},
     number = {3},
     year = {2007},
     mrnumber = {2356935},
     zbl = {1174.76008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007__57_3_a15/}
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Gao, Zhiming; Ma, Yichen; Zhuang, Hongwei. Shape Hessian for generalized Oseen flow by differentiability of a minimax: A Lagrangian approach. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 987-1011. http://geodesic.mathdoc.fr/item/CMJ_2007__57_3_a15/