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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.

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