On an optimal shape design problem in conduction
2006 - J. C. Bellido
ESAIM-Control Optimization and Calculus of Variations 12, 699-720 (2006).
In this paper we analyze a typical shape optimization problem in two-dimensional conductivity. We study relaxation for this problem itself. We also analyze the question of the approximation of this problem by the two-phase optimal design problems obtained when we fill out the holes that we want to design in the original problem by a very poor conductor, that we make to converge to zero.