Domain Optimization Analysis of Continua
Since Hadamard  showed the differentiability of perturbations of a geometrical domain with a smooth boundary in which an elliptic boundary value problem is defined, many researchers have made clear the theory concerning geometrical domain optimization problems   . Theoretical expansion to domains with piecewise smooth boundaries was carried out by Zolésio  . He formulated domain perturbations with a smooth transformation, or mapping, of Euclidean space just the same as the original domain. He called the domain perturbation the speed field and this approach the speed method, or the material derivative method.
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