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Journal of Convex Analysis 21 (2014), No. 1, 067--087
Copyright Heldermann Verlag 2014

On a Shape Derivative Formula with Respect to Convex Domains

Abdesslam Boulkhemair
Lab. de Mathématiques Jean Leray, Université de Nantes, 2, rue de la Houssinière, 44322 Nantes, France

Abdelkrim Chakib
Lab. de Mathématiques et Applications, FST de Beni-Mellal, Université Sultan Moulay Slimane, B.P. 523, Beni-Mellal, Morocco

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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