Abstract:
We study the eigenvalue problem for a system of fractional p-Laplacians, that is, (-Δp)ru=λαp|u|α-2u|v|β(-Δp)sv=λβp|u|α|v|β-2vu=v=0in Ω,in Ω,in Ωc=RN\\Ω. We show that there is a first (smallest) eigenvalue that is simple and has associated eigenpairs composed of positive and bounded functions. Moreover, there is a sequence of eigenvalues λn such that λn→∞ as n→∞ . In addition, we study the limit as p→∞ of the first eigenvalue, λ1,p, and we obtain [λ1,p]1/p→Λ1,∞ as p→∞, where Λ1,∞=inf(u,v){max{[u]r,∞[v]s,∞}∥|u|Γ|v|1-Γ∥L∞(Ω)}=[1R(Ω)](1-Γ)s+Γr. Here, R(Ω):= maxx∈Ω dist(x,∂Ω) and [w]t,∞:=sup(x,y)∈Ω|w(y)-w(x)||x-y|t. Finally, we identify a PDE problem satisfied, in the viscosity sense, by any possible uniform limit along subsequences of the eigenpairs. Copyright © 2018 Rocky Mountain Mathematics Consortium.
Registro:
Documento: |
Artículo
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Título: | Eigenvalues for systems of fractional p-Laplacians |
Autor: | Del Pezzo, L.M.; Rossi, J.D. |
Filiación: | Departamento de Matematicas Y Estadistica, Av. Figueroa, Alcorta, 7350, Argentina Conicet and Departamento de Matematica, Universidad de Buenos Aires, Pabellon I, Buenos Aires, Argentina
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Palabras clave: | Eigenvalue problems; Fractional operators; P-laplacian |
Año: | 2018
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Volumen: | 48
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Número: | 4
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Página de inicio: | 1077
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Página de fin: | 1104
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DOI: |
http://dx.doi.org/10.1216/RMJ-2018-48-4-1077 |
Título revista: | Rocky Mountain Journal of Mathematics
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Título revista abreviado: | Rocky Mt. J. Math.
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ISSN: | 00357596
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00357596_v48_n4_p1077_DelPezzo |
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Citas:
---------- APA ----------
Del Pezzo, L.M. & Rossi, J.D.
(2018)
. Eigenvalues for systems of fractional p-Laplacians. Rocky Mountain Journal of Mathematics, 48(4), 1077-1104.
http://dx.doi.org/10.1216/RMJ-2018-48-4-1077---------- CHICAGO ----------
Del Pezzo, L.M., Rossi, J.D.
"Eigenvalues for systems of fractional p-Laplacians"
. Rocky Mountain Journal of Mathematics 48, no. 4
(2018) : 1077-1104.
http://dx.doi.org/10.1216/RMJ-2018-48-4-1077---------- MLA ----------
Del Pezzo, L.M., Rossi, J.D.
"Eigenvalues for systems of fractional p-Laplacians"
. Rocky Mountain Journal of Mathematics, vol. 48, no. 4, 2018, pp. 1077-1104.
http://dx.doi.org/10.1216/RMJ-2018-48-4-1077---------- VANCOUVER ----------
Del Pezzo, L.M., Rossi, J.D. Eigenvalues for systems of fractional p-Laplacians. Rocky Mt. J. Math. 2018;48(4):1077-1104.
http://dx.doi.org/10.1216/RMJ-2018-48-4-1077