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Velocity method and Lagrangian formulation for the computation of the shape Hessian. (English) Zbl 0747.49007
The authors study the shape Hessian of a shape functional by the velocity method. A shape functional is a function defined on a suitable class of subsets of $$\mathbb{R}^ n$$ and the shape Hessian is the second derivative of this function as the domain is perturbed via a smooth non-degenerate vector field. The properties of the shape Hessian are used to examine various optimization problems in which the domain varies.

##### MSC:
 49J20 Existence theories for optimal control problems involving partial differential equations
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