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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todo:paper_09262601_v48_n3_p361_Pereira2023-10-03T15:46:34Z An Obstacle Problem for Nonlocal Equations in Perforated Domains Pereira, M.C. Rossi, J.D. Dirichlet problem Neumann problem Nonlocal equations 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 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. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_09262601_v48_n3_p361_Pereira |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Dirichlet problem Neumann problem Nonlocal equations Perforated domains |
| spellingShingle |
Dirichlet problem Neumann problem Nonlocal equations Perforated domains Pereira, M.C. Rossi, J.D. An Obstacle Problem for Nonlocal Equations in Perforated Domains |
| topic_facet |
Dirichlet problem Neumann problem Nonlocal equations Perforated domains |
| description |
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. |
| format |
JOUR |
| author |
Pereira, M.C. Rossi, J.D. |
| author_facet |
Pereira, M.C. Rossi, J.D. |
| author_sort |
Pereira, M.C. |
| title |
An Obstacle Problem for Nonlocal Equations in Perforated Domains |
| title_short |
An Obstacle Problem for Nonlocal Equations in Perforated Domains |
| title_full |
An Obstacle Problem for Nonlocal Equations in Perforated Domains |
| title_fullStr |
An Obstacle Problem for Nonlocal Equations in Perforated Domains |
| title_full_unstemmed |
An Obstacle Problem for Nonlocal Equations in Perforated Domains |
| title_sort |
obstacle problem for nonlocal equations in perforated domains |
| url |
http://hdl.handle.net/20.500.12110/paper_09262601_v48_n3_p361_Pereira |
| work_keys_str_mv |
AT pereiramc anobstacleproblemfornonlocalequationsinperforateddomains AT rossijd anobstacleproblemfornonlocalequationsinperforateddomains AT pereiramc obstacleproblemfornonlocalequationsinperforateddomains AT rossijd obstacleproblemfornonlocalequationsinperforateddomains |
| _version_ |
1807319105202552832 |