An Obstacle Problem for Nonlocal Equations in Perforated Domains
In this paper we analyze the behavior of solutions to a nonlocal equation of the form J ∗ u (x) − u (x) = f (x) in a perforated domain Ω ∖ Aϵ with u = 0 in Aϵ∪ Ω c and an obstacle constraint, u ≥ ψ in Ω ∖ Aϵ. We show that, assuming that the characteristic function of the domain Ω ∖ Aϵ verifies χϵ⇀ X...
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| Autores principales: | , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_09262601_v48_n3_p361_Pereira |
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| Sumario: | In this paper we analyze the behavior of solutions to a nonlocal equation of the form J ∗ u (x) − u (x) = f (x) in a perforated domain Ω ∖ Aϵ with u = 0 in Aϵ∪ Ω c and an obstacle constraint, u ≥ ψ in Ω ∖ Aϵ. We show that, assuming that the characteristic function of the domain Ω ∖ Aϵ verifies χϵ⇀ X weakly ∗ in L∞(Ω) , there exists a weak limit of the solutions uϵ and we find the limit problem that is satisfied in the limit. When X≢ 1 in this limit problem an extra term appears in the equation as well as a modification of the obstacle constraint inside the domain. © 2017, Springer Science+Business Media B.V. |
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