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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2106.06031 |
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Table of Contents:
- We explore the dual approach to nonlocal optimal design, specifically for a classical min-max problem which in this study is associated with a nonlocal scalar diffusion equation. We reformulate the optimal design problem utilizing a dual variational principle, which is expressed in terms of nonlocal two-point fluxes. We introduce the proper functional space framework to deal with this formulation, and establish its well-posedness. The key ingredient is the inf-sup (Ladyzhenskaya--Babuska--Brezzi) condition, which holds uniformly with respect to small nonlocal horizons. As a byproduct of this, we are able to prove convergence of nonlocal to local optimal design problems in a straightforward fashion.