Existence of an optimal domain in a domain optimization problem

Existence of an optimal domain in a domain optimization problem is studied. By a domain optimization problem we denote an optimization problem in which an object function depending on the domain through the solution of the boundary value problem defined on the domain should be optimized. A new class of domains and a new notion of convergence of domains are introduced. With these new notions the lower semicontinuity results show the existence of an optimal domain for a wide class of optimization problems; the solution of the Dirichlet problem corresponding to the domain is a genuine (classical) solution.