Abstract
In optimal shape problems the derivatives of costs with respect to shapes are important, because it gives a direction of lower cost from an initial shape. The differentiability of costs strongly depends on shape derivatives of solutions of mechanical problems, stationary linearized flow problems, the Stokes problems. The shape derivatives are usually given automatically by the associated material derivatives. We show the convergence of shape difference quotients under sufficient conditions. These conditions are applied to the existence of the shape derivatives of the velocity and the pressure in the Stokes problems.
