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Abstract:

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.

Registro:

Documento: Artículo
Título:An Obstacle Problem for Nonlocal Equations in Perforated Domains
Autor:Pereira, M.C.; Rossi, J.D.
Filiación:Dpto. de Matemática Aplicada, IME, Universidade de São Paulo, Rua do Matão 1010, São Paulo, SP, Brazil
Dpto. de Matemáticas, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria Pab 1, Buenos Aires, 1428, Argentina
Palabras clave:Dirichlet problem; Neumann problem; Nonlocal equations; Perforated domains
Año:2018
Volumen:48
Número:3
Página de inicio:361
Página de fin:373
DOI: http://dx.doi.org/10.1007/s11118-017-9639-5
Título revista:Potential Analysis
Título revista abreviado:Potential Anal.
ISSN:09262601
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09262601_v48_n3_p361_Pereira

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Citas:

---------- APA ----------
Pereira, M.C. & Rossi, J.D. (2018) . An Obstacle Problem for Nonlocal Equations in Perforated Domains. Potential Analysis, 48(3), 361-373.
http://dx.doi.org/10.1007/s11118-017-9639-5
---------- CHICAGO ----------
Pereira, M.C., Rossi, J.D. "An Obstacle Problem for Nonlocal Equations in Perforated Domains" . Potential Analysis 48, no. 3 (2018) : 361-373.
http://dx.doi.org/10.1007/s11118-017-9639-5
---------- MLA ----------
Pereira, M.C., Rossi, J.D. "An Obstacle Problem for Nonlocal Equations in Perforated Domains" . Potential Analysis, vol. 48, no. 3, 2018, pp. 361-373.
http://dx.doi.org/10.1007/s11118-017-9639-5
---------- VANCOUVER ----------
Pereira, M.C., Rossi, J.D. An Obstacle Problem for Nonlocal Equations in Perforated Domains. Potential Anal. 2018;48(3):361-373.
http://dx.doi.org/10.1007/s11118-017-9639-5