Erratum. On a Shape Derivative Formula with Respect to Convex Domains

In a previous article of the authors [Journal of Convex Analysis 21 (2014) 67–87], we extended to the case of $W^{1,1}_{\mathrm{loc}}$ 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 above-mentioned article remain valid.