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Young Women in Harmonic Analysis and PDE

December 2-4, 2016

Ivana Crnjac (University of Osijek)

Variant of optimality criteria method for multiple state optimal design problems

In the multiple state optimal design problems, one is trying to find the best arrangement of given materials, such that the obtained body has some optimal properties regarding different regimes.The performance of the mixture is measured by an objective function which is an integral functional. We consider mixtures of two isotropic materials in context of stationary diffusion equation. It is well known that these problems do not admit classical solution, therefore we use relaxation by homogenization method. We rewrite optimality conditions for relaxed problem in order to apply optimality criteria method to multiple state problems in three dimensions. This problem was considered by Vrdoljak (2010), but optimality criteria method didn't give converging sequence of designs for some energy minimization problems. We present another variant of optimality criteria method that can be applied to those problems as well. This is joint work with Kre\v simir Burazin and Marko Vrdoljak.