English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We derive the dual variational principle (principle of minimal complementaryenergy) for the nonlocal nonlinear scalar diffusion problem, which may beviewed as the nonlocal version of the $p$-Laplacian operator. We establishexistence and uniqueness of solutions (two-point fluxes) as well as theirquantitative stability, which holds uniformly with respect to the smallparameter (nonlocal horizon) characterizing the nonlocality of the problem. Wethen focus on the nonlocal analogue of the classical optimal control in thecoefficient problem associated with the dual variational principle, which maybe interpreted as that of optimally distributing a limited amount ofconductivity in order to minimize the complementary energy. We show that thisnonlocal optimal control problem $\Gamma$-converges to its local counterpart,when the nonlocal horizon vanishes.

The dual approach to optimal control in the coefficients of nonlocal nonlinear diffusion