Geodesic
Structure of Shape Derivatives Around Irregular Domains and Applications
Journal of convex analysis, Tome 14 (2007) no. 4, pp. 807-822.

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We describe the structure of shape derivatives around sets which are only assumed to be of finite perimeter in the real N-dimensional space RN. This structure allows us to define a useful notion of positivity of the shape derivative and we show it implies its continuity with respect to the uniform norm when the boundary is Lipschitz (this restriction is essentially optimal). We apply this idea to various cases including the perimeter-type functionals for convex and pseudo-convex shapes or the Dirichlet energy of an open set.
Mots-clés : Shape optimization, shape derivatives, sets of finite perimeter, convex sets, Dirichlet energy 
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     author = {J. Lamboley and M. Pierre},
     title = {Structure of {Shape} {Derivatives} {Around} {Irregular} {Domains} and {Applications}},
     journal = {Journal of convex analysis},
     pages = {807--822},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2007},
     url = {http://geodesic.mathdoc.fr/item/JCA_2007_14_4_JCA_2007_14_4_a6/}
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J. Lamboley; M. Pierre. Structure of Shape Derivatives Around Irregular Domains and Applications. Journal of convex analysis, Tome 14 (2007) no. 4, pp. 807-822. http://geodesic.mathdoc.fr/item/JCA_2007_14_4_JCA_2007_14_4_a6/