Pereira, M.C.; Rossi, J.D."Nonlocal problems in thin domains" (2017) Journal of Differential Equations. 263(3):1725-1754
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In this paper we consider nonlocal problems in thin domains. First, we deal with a nonlocal Neumann problem, that is, we study the behavior of the solutions to f(x)=∫Ω1×Ω2Jϵ(x−y)(uϵ(y)−uϵ(x))dy with Jϵ(z)=J(z1,ϵz2) and Ω=Ω1×Ω2⊂RN=RN1×RN2 a bounded domain. We find that there is a limit problem, that is, we show that uϵ→u0 as ϵ→0 in Ω and this limit function verifies ∫Ω2f(x1,x2)dx2=|Ω2|∫Ω1J(x1−y1,0)(U0(y1)−U0(x1))dy1, with U0(x1)=∫Ω2u0(x1,x2)dx2. In addition, we deal with a double limit when we add to this model a rescale in the kernel with a parameter that controls the size of the support of J. We show that this double limit exhibits some interesting features. We also study a nonlocal Dirichlet problem f(x)=∫RNJϵ(x−y)(uϵ(y)−uϵ(x))dy, x∈Ω, with uϵ(x)≡0, x∈RN∖Ω, and deal with similar issues. In this case the limit as ϵ→0 is u0=0 and the double limit problem commutes and also gives v≡0 at the end. © 2017 Elsevier Inc.


Documento: Artículo
Título:Nonlocal problems in thin 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, Buenos Aires, 1428, Argentina
Palabras clave:Dirichlet problem; Neumann problem; Nonlocal equations; Thin domains
Página de inicio:1725
Página de fin:1754
Título revista:Journal of Differential Equations
Título revista abreviado:J. Differ. Equ.


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---------- APA ----------
Pereira, M.C. & Rossi, J.D. (2017) . Nonlocal problems in thin domains. Journal of Differential Equations, 263(3), 1725-1754.
---------- CHICAGO ----------
Pereira, M.C., Rossi, J.D. "Nonlocal problems in thin domains" . Journal of Differential Equations 263, no. 3 (2017) : 1725-1754.
---------- MLA ----------
Pereira, M.C., Rossi, J.D. "Nonlocal problems in thin domains" . Journal of Differential Equations, vol. 263, no. 3, 2017, pp. 1725-1754.
---------- VANCOUVER ----------
Pereira, M.C., Rossi, J.D. Nonlocal problems in thin domains. J. Differ. Equ. 2017;263(3):1725-1754.