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Nonlocal problems in perforated domains
In this paper we analyze nonlocal equations in perforated domains. We consider nonlocal problems of the form $f(x) = \int_{B} J(x-y) (u(y) - u(x)) dy$ with $x$ in a perforated domain $Ω^ε\subset Ω$. Here $J$ is a non-singular kernel. We think about $Ω^ε$ as a fixed set $Ω$ from where …