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Abstract:

In this work we consider the maximum and antimaximum principles for the nonlocal Dirichlet problem J * u - u + λ u + h = ∫RN J (x - y) u (y) d y - u (x) + λ u (x) + h (x) = 0 in a bounded domain Ω, with u (x) = 0 in RN {set minus} Ω. The kernel J in the convolution is assumed to be a continuous, compactly supported nonnegative function with unit integral. We prove that for λ < λ1 (Ω), the solution verifies u > 0 in over(Ω, -) if h ∈ L2 (Ω), h ≥ 0, while for λ > λ1 (Ω), and λ close to λ1 (Ω), the solution verifies u < 0 in over(Ω, -), provided ∫Ω h (x) φ{symbol} (x) d x > 0, h ∈ L∞ (Ω). This last assumption is also shown to be optimal. The "Neumann" version of the problem is also analyzed. © 2009 Elsevier Ltd. All rights reserved.

Registro:

Documento: Artículo
Título:Maximum and antimaximum principles for some nonlocal diffusion operators
Autor:García-Melián, J.; Rossi, J.D.
Filiación:Departamento de Análisis Matemático, Universidad de La Laguna, C/. Astrofisico Francisco Sanchez s/n, 38271 La Laguna, Spain
Instituto Universitario de Estudios Avanzados (IUdEA) en Física Atómica, Molecular y Fotónica, Facultad de Física, C/. Astrofisico Francisco Sanchez s/n, 38203 La Laguna, Spain
Dpto. de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Antimaximum principle; Maximum principle; Nonlocal diffusion; Principal eigenvalue; Bounded domain; Compactly supported; Dirichlet problem; Nonlocal; Nonlocal diffusion; Nonnegative functions; Principal eigenvalues; Diffusion; Maximum principle; Eigenvalues and eigenfunctions
Año:2009
Volumen:71
Número:12
Página de inicio:6116
Página de fin:6121
DOI: http://dx.doi.org/10.1016/j.na.2009.06.004
Título revista:Nonlinear Analysis, Theory, Methods and Applications
Título revista abreviado:Nonlinear Anal Theory Methods Appl
ISSN:0362546X
CODEN:NOAND
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v71_n12_p6116_GarciaMelian

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Citas:

---------- APA ----------
García-Melián, J. & Rossi, J.D. (2009) . Maximum and antimaximum principles for some nonlocal diffusion operators. Nonlinear Analysis, Theory, Methods and Applications, 71(12), 6116-6121.
http://dx.doi.org/10.1016/j.na.2009.06.004
---------- CHICAGO ----------
García-Melián, J., Rossi, J.D. "Maximum and antimaximum principles for some nonlocal diffusion operators" . Nonlinear Analysis, Theory, Methods and Applications 71, no. 12 (2009) : 6116-6121.
http://dx.doi.org/10.1016/j.na.2009.06.004
---------- MLA ----------
García-Melián, J., Rossi, J.D. "Maximum and antimaximum principles for some nonlocal diffusion operators" . Nonlinear Analysis, Theory, Methods and Applications, vol. 71, no. 12, 2009, pp. 6116-6121.
http://dx.doi.org/10.1016/j.na.2009.06.004
---------- VANCOUVER ----------
García-Melián, J., Rossi, J.D. Maximum and antimaximum principles for some nonlocal diffusion operators. Nonlinear Anal Theory Methods Appl. 2009;71(12):6116-6121.
http://dx.doi.org/10.1016/j.na.2009.06.004