  We consider the optimization problem for a shape cost functional
$F(\Omega,f)$ which depends on a domain $\Omega$ varying in a suitable
admissible class and on a "right-hand side" $f$. More precisely, the cost
functional $F$ is given by an integral which involves the solution $u$ of an
elliptic PDE in $\Omega$ with right-hand side $f$; the boundary conditions
considered are of the Dirichlet type. When the function $f$ is only known up to
some degree of uncertainty, our goal is to obtain the existence of an optimal
shape in the worst possible situation. Some numerical simulations are provided,
showing the difference in the optimal shape between the case when $f$ is
perfectly known and the case when only the worst situation is optimized.
