Maximum and antimaximum principles for some nonlocal diffusion operators

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, com...

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Autores principales:	García-Melián, J., Rossi, J.D.
Formato:	JOUR
Materias:	Antimaximum principle Maximum principle Nonlocal diffusion Principal eigenvalue Bounded domain Compactly supported Dirichlet problem Nonlocal Nonnegative functions Principal eigenvalues Diffusion Eigenvalues and eigenfunctions
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_0362546X_v71_n12_p6116_GarciaMelian
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_0362546X_v71_n12_p6116_GarciaMelian
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spelling	todo:paper_0362546X_v71_n12_p6116_GarciaMelian2023-10-03T15:27:21Z Maximum and antimaximum principles for some nonlocal diffusion operators García-Melián, J. Rossi, J.D. 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 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. 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_0362546X_v71_n12_p6116_GarciaMelian
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	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
spellingShingle	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 García-Melián, J. Rossi, J.D. Maximum and antimaximum principles for some nonlocal diffusion operators
topic_facet	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
description	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.
format	JOUR
author	García-Melián, J. Rossi, J.D.
author_facet	García-Melián, J. Rossi, J.D.
author_sort	García-Melián, J.
title	Maximum and antimaximum principles for some nonlocal diffusion operators
title_short	Maximum and antimaximum principles for some nonlocal diffusion operators
title_full	Maximum and antimaximum principles for some nonlocal diffusion operators
title_fullStr	Maximum and antimaximum principles for some nonlocal diffusion operators
title_full_unstemmed	Maximum and antimaximum principles for some nonlocal diffusion operators
title_sort	maximum and antimaximum principles for some nonlocal diffusion operators
url	http://hdl.handle.net/20.500.12110/paper_0362546X_v71_n12_p6116_GarciaMelian
work_keys_str_mv	AT garciamelianj maximumandantimaximumprinciplesforsomenonlocaldiffusionoperators AT rossijd maximumandantimaximumprinciplesforsomenonlocaldiffusionoperators
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Maximum and antimaximum principles for some nonlocal diffusion operators

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