Titlebook: Optimal Design of Multi-Phase Materials; With a Cost Function Juan Casado-Díaz Book 2022 The Author(s), under exclusive license to Springer

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,Homogenization of Elliptic PDE with?Varying Coefficients,o know some projections of this set. We are mainly interested in the case where we start with a finite number of materials, not necessarily isotropic, which are represented by their corresponding diffusion matrices.

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The Relaxed Formulation of an Optimal Design Problem via Homogenization Theory,sion matrices. It consists in obtaining a matrix function in a bounded open set . by placing in each point one of the materials in such way that the corresponding electric potential or temperature minimizes a certain functional. It is well known that this problem has no solution in general and there

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Optimality Conditions and Numerical Resolution,ing in general an explicit representation of the functional which appears in the relaxed formulation. To solve it we propose some strategies consisting in replacing this functional by an upper or a lower approximation. This uses the knowledge of this functional obtained in Chap.?.. We also show the

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Some Extesions: Multi-state and Evolutive Problems,ly finite, of state equations. From the application point of view this means that we are interested in obtaining a material which works well in several situations being more stable with respect to the variation of the external conditions. Unfortunately, this introduces several difficulties such as t