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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Detalles Bibliográficos
Autor principal: Rossi, Julio Daniel
Publicado: 2009
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:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v71_n12_p6116_GarciaMelian
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 paper:paper_0362546X_v71_n12_p6116_GarciaMelian
record_format dspace
spelling paper:paper_0362546X_v71_n12_p6116_GarciaMelian2023-06-08T15:35:22Z Maximum and antimaximum principles for some nonlocal diffusion operators Rossi, Julio Daniel 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. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v71_n12_p6116_GarciaMelian 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
Rossi, Julio Daniel
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.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
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
publishDate 2009
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v71_n12_p6116_GarciaMelian
http://hdl.handle.net/20.500.12110/paper_0362546X_v71_n12_p6116_GarciaMelian
work_keys_str_mv AT rossijuliodaniel maximumandantimaximumprinciplesforsomenonlocaldiffusionoperators
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