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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2009
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| 003 | AR-BaUEN | ||
| 005 | 20230518203802.0 | ||
| 008 | 190411s2009 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-72149096525 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 030 | |a NOAND | ||
| 100 | 1 | |a García-Melián, J. | |
| 245 | 1 | 0 | |a Maximum and antimaximum principles for some nonlocal diffusion operators |
| 260 | |c 2009 | ||
| 270 | 1 | 0 | |m García-Melián, J.; Departamento de Análisis Matemático, Universidad de La Laguna, C/. Astrofisico Francisco Sanchez s/n, 38271 La Laguna, Spain; email: jjgarmel@ull.es |
| 506 | |2 openaire |e Política editorial | ||
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| 520 | 3 | |a 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. |l eng | |
| 536 | |a Detalles de la financiación: Ministerio de Educación y Cultura | ||
| 536 | |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas, UBA X066 | ||
| 536 | |a Detalles de la financiación: Federación Española de Enfermedades Raras, FEDER, MTM2008-05824 | ||
| 536 | |a Detalles de la financiación: Partially supported by MEC and FEDER under grant MTM2008-05824 (Spain), CONICET (Argentina) and UBA X066 (Argentina). | ||
| 593 | |a Departamento de Análisis Matemático, Universidad de La Laguna, C/. Astrofisico Francisco Sanchez s/n, 38271 La Laguna, Spain | ||
| 593 | |a 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 | ||
| 593 | |a Dpto. de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a ANTIMAXIMUM PRINCIPLE |
| 690 | 1 | 0 | |a MAXIMUM PRINCIPLE |
| 690 | 1 | 0 | |a NONLOCAL DIFFUSION |
| 690 | 1 | 0 | |a PRINCIPAL EIGENVALUE |
| 690 | 1 | 0 | |a BOUNDED DOMAIN |
| 690 | 1 | 0 | |a COMPACTLY SUPPORTED |
| 690 | 1 | 0 | |a DIRICHLET PROBLEM |
| 690 | 1 | 0 | |a NONLOCAL |
| 690 | 1 | 0 | |a NONLOCAL DIFFUSION |
| 690 | 1 | 0 | |a NONNEGATIVE FUNCTIONS |
| 690 | 1 | 0 | |a PRINCIPAL EIGENVALUES |
| 690 | 1 | 0 | |a DIFFUSION |
| 690 | 1 | 0 | |a MAXIMUM PRINCIPLE |
| 690 | 1 | 0 | |a EIGENVALUES AND EIGENFUNCTIONS |
| 700 | 1 | |a Rossi, J.D. | |
| 773 | 0 | |d 2009 |g v. 71 |h pp. 6116-6121 |k n. 12 |p Nonlinear Anal Theory Methods Appl |x 0362546X |w (AR-BaUEN)CENRE-254 |t Nonlinear Analysis, Theory, Methods and Applications | |
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