Geodesic
On a Shape Derivative Formula with Respect to Convex Domains
Journal of convex analysis, Tome 21 (2014) no. 1, pp. 67-87.

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We extend to the case of W1,1loc functions a formula, known for C1 functions, for the computation of the shape derivative of an integral cost functional with respect to a class of admissible convex domains. The convexity context allows one to use the support functions of the domains to express the shape derivative. We shall also illustrate the formula by applying it to the computation of the shape derivative for a shape optimization problem and by giving an algorithm. 
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     author = {A. Boulkhemair and A. Chakib},
     title = {On a {Shape} {Derivative} {Formula} with {Respect} to {Convex} {Domains}},
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     pages = {67--87},
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A. Boulkhemair; A. Chakib. On a Shape Derivative Formula with Respect to Convex Domains. Journal of convex analysis, Tome 21 (2014) no. 1, pp. 67-87. http://geodesic.mathdoc.fr/item/JCA_2014_21_1_JCA_2014_21_1_a3/