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Topological Optimization and Optimal Transport by Filippo Santambrogio, Thierry Champion, Guillaume Carlier, Martin Rumpf, Édouard Oudet, Maïtine Bergounioux

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Plugging the representation (3.52c) in (3.47), we establish the following equivalence.

Proposition 3.8. The topology optimization problem (3.48) can be equivalently stated with respect to the primal and dual state variables. Find (ω*, ε*, x*) ∈ such that

Further we provide asymptotic analysis of the objective as ε ↘ +0.

As ε = 0, problem (3.51 ...

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