Pereira, M.C.; Rossi, J.D.; Saintier, N. "Fractional problems in thin domains" (2019) Nonlinear Analysis, Theory, Methods and Applications
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In this paper we consider nonlocal fractional problems in thin domains. Given open bounded subsets U⊂R n and V⊂R m , we show that the solution u ε to Δ x s u ε (x,y)+Δ y t u ε (x,y)=f(x,ε −1 y)inU×εV with u ε (x,y)=0 if x⁄∈U and y∈εV, verifies that ũ ε (x,y)≔u ε (x,εy)→u 0 strongly in the natural fractional Sobolev space associated to this problem. We also identify the limit problem that is satisfied by u 0 and estimate the rate of convergence in the uniform norm. Here Δ x s u and Δ y t u are the fractional Laplacian in the 1st variable x (with a Dirichlet condition, u(x)=0 if x⁄∈U) and in the 2nd variable y (with a Neumann condition, integrating only inside V), respectively, that is, Δ x s u(x,y)=∫ R n [Formula presented]dw and Δ y t u(x,y)=∫ V [Formula presented]dz. © 2019 Elsevier Ltd


Documento: Artículo
Título:Fractional problems in thin domains
Autor:Pereira, M.C.; Rossi, J.D.; Saintier, N.
Filiación:Dpto. de Matemática Aplicada, IME, Universidade de São Paulo, Rua do Matão, São Paulo - SP 1010, Brazil
Dpto. de Matemáticas, FCEyN, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
Palabras clave:Dirichlet problem; Neumann problem; Nonlocal fractional equations; Thin domains; Boundary value problems; Dirichlet condition; Dirichlet problem; Fractional equation; Fractional Laplacian; Neumann problem; Open bounded subsets; Rate of convergence; Thin domains; Sobolev spaces
Título revista:Nonlinear Analysis, Theory, Methods and Applications
Título revista abreviado:Nonlinear Anal Theory Methods Appl


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---------- APA ----------
Pereira, M.C., Rossi, J.D. & Saintier, N. (2019) . Fractional problems in thin domains. Nonlinear Analysis, Theory, Methods and Applications.
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Pereira, M.C., Rossi, J.D., Saintier, N. "Fractional problems in thin domains" . Nonlinear Analysis, Theory, Methods and Applications (2019).
---------- MLA ----------
Pereira, M.C., Rossi, J.D., Saintier, N. "Fractional problems in thin domains" . Nonlinear Analysis, Theory, Methods and Applications, 2019.
---------- VANCOUVER ----------
Pereira, M.C., Rossi, J.D., Saintier, N. Fractional problems in thin domains. Nonlinear Anal Theory Methods Appl. 2019.