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Journal of Convex Analysis 22 (2015), No. 3, 901--903
Copyright Heldermann Verlag 2015

Erratum. 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

In a previous article of the authors [Journal of Convex Analysis 21 (2014) 67--87], we extended 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 convex domains. The interest in that formula was that, due to the convexity context, it uses the support functions of the domains to express the shape derivative. Unfortunately, we noticed after the publication that we made a mistake in the proof of the main result. In this Erratum we give an alternative argument so that all the results in the above-mentioned article remain valid.

Keywords: Shape derivative, integral cost functional, convex domains, erratum, Sobolev space, support function, gauge function, Hausdorff distance.

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