Double control problem: domains and coefficients for elliptic equations

Abstract

In this work we are interested in a bi-optimal control problem for a linear elliptic state equation with homogeneous boundary Dirichlet condition. The two controls variables correspond to the coefficient of the diffusion term of the equation and the open set where the it is posed. From the practical point of view, this problem can be interpreted as finding materials from the mixture of other ones with different diffusion properties and on optimal shape. We analyze a relaxation process, optimality conditions, and finally we provide a numerical algorithm and we show some numerical experiments.