Differentiation with Respect to Domains of Boundary Integral Functionals Involving Support Functions.

The aim of this paper is to establish a new formula for the computation of the shape derivative of boundary integral cost functionals using Minkowski deformation of star-shaped domains by convex ones. The formula is expressed by means of the support function of the convex domain. The proof uses some geometrical tools in addition to an analysis of star-shapedness involving gauge functions. Finally, in order to illustrate this result, the formula is applied for solving an optimal shape design problem of minimizing a surface cost functional constrained to elliptic boundary value problem, using the gradient method performed by the finite element approximation. [ABSTRACT FROM AUTHOR]