SHAPE OPTIMIZATION PROBLEMS GOVERNED BY NONLINEAR STATE-EQUATIONS

The purpose of this paper is to give a compactness-continuity result f or the solution of a nonlinear Dirichlet problem in terms of its domai n variation. The topology in the family of domains is given by the Hau sdorff metric and continuity is obtained under capacity conditions. A generalisation of Sverak's result in N-dimensions is deduced as a part icular case.