A shape optimization problem is defined as an optimization problem to boundary shape of domain in which boundary value problem of partial differential equation is defined. A design variable is given by a domain mapping. Cost functions are defined as functionals of the design variable and the solution to the boundary value problem. The present paper described that the Frechet derivatives of cost functions with respect to domain variation do not have the regularity required in order to define a next domain, and that a gradient method can be considered for regularizing the derivatives.