Abstract
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.
Original language | English |
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Publisher | arXiv |
Edition | arXiv:2106.06031 |
Volume | math.OC |
Number of pages | 13 |
Publication status | Published - 10 Jun 2021 |