On the existence of the shape derivative of solutions of boundary value problems using Minkowski deformation

<div> In this work, we show the existence of the shape derivative of the solution of Laplacian Dirichlet and Neumann boundary value problems using the Minkowski deformation of convex domains by convex ones. We also illustrate this result by applying it to the computation of the shape derivative of some more or less standard cost functionals that depend on solutions of boundary value problems. </div>