
Journal of Convex Analysis 22 (2015), No. 3, 901903 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 boulkhemaira@univnantes.fr Abdelkrim Chakib Lab. de Mathématiques et Applications, FST de BeniMellal, Université Sultan Moulay Slimane, B.P. 523, BeniMellal, Morocco chakib@fstbm.ac.ma In a previous article of the authors [Journal of Convex Analysis 21 (2014) 6787], we extended to the case of W^{1,1}_{loc} functions a formula, known for C^{1} 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 abovementioned article remain valid. Keywords: Shape derivative, integral cost functional, convex domains, erratum, Sobolev space, support function, gauge function, Hausdorff distance. [ Fulltextpdf (77 KB)] for subscribers only. 