Geodesic
A structure theorem for shape functions defined on submanifolds
Kevin Sturm1
1Universität Duisburg-Essen, Germany
Interfaces and free boundaries, Tome 18 (2016) no. 4, pp. 523-543

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DOI

In this paper, we study shape functions depending on closed submanifolds. We prove a new structure theorem that establishes the general structure of the shape derivative for this type of shape function. As a special case we obtain the classical Hadamard–Zolésio structure theorem, but also the structure theorem for cracked sets can be recast into our framework. As an application we investigate several unconstrained shape functions arising from differential geometry and fracture mechanics.
DOI : 10.4171/ifb/372
Classification : 49-XX, 90-XX
Mots-clés : Shape optimisation, submanifolds, structure theorem

Kevin Sturm  1

1 Universität Duisburg-Essen, Germany 
Kevin Sturm. A structure theorem for shape functions defined on submanifolds. Interfaces and free boundaries, Tome 18 (2016) no. 4, pp. 523-543. doi: 10.4171/ifb/372
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     number = {4},
     doi = {10.4171/ifb/372},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/372/}
}
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