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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
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
Palabras clave:Eigenvalue problems; Fractional operators; P-laplacian
Año:2018
Volumen:48
Número:4
Página de inicio:1077
Página de fin:1104
DOI: http://dx.doi.org/10.1216/RMJ-2018-48-4-1077
Título revista:Rocky Mountain Journal of Mathematics
Título revista abreviado:Rocky Mt. J. Math.
ISSN:00357596
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