SHAPE AND TOPOLOGICAL OPTIMIZATION OF A NONLINEAR ELLIPTICAL PROBLEM

In this work, let us deal with existence and derivation results in shape optimization. It should be noted that a shape optimization problem does not generally have a solution with only its initial data. To get around the non-existence of solution, we impose geometric order restrictions (i.e. volume type) and we work with the open class checking the cone property to obtain existence. On the other hand, we determine the shape derivative using the Lagrange method. And then we establish the topological derivative using the minmax method.