Abstract:
In this paper we study the eigenvalue problems for a nonlocal operator of order s that is analogous to the local pseudo p-Laplacian. We show that there is a sequence of eigenvalues λn→ ∞and that the first one is positive, simple, isolated and has a positive and bounded associated eigenfunction. For the first eigenvalue we also analyze the limits as p → ∞ (obtaining a limit nonlocal eigenvalue problem analogous to the pseudo infinity Laplacian) and as s → 1- (obtaining the first eigenvalue for a local operator of p-Laplacian type). To perform this study we have to introduce anisotropic fractional Sobolev spaces and prove some of their properties.
Registro:
Documento: |
Artículo
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Título: | Eigenvalues for a nonlocal pseudo p-Laplacian |
Autor: | Del Pezzo, L.M.; Rossi, J.D. |
Filiación: | CONICET, Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellon i, Ciudad Universitaria, Buenos Aires, 1428, Argentina
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Palabras clave: | Asymptotic behavior; Dirichlet boundary conditions; Eigenvalues; Nonlocal operator |
Año: | 2016
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Volumen: | 36
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Número: | 12
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Página de inicio: | 6737
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Página de fin: | 6765
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DOI: |
http://dx.doi.org/10.3934/dcds.2016093 |
Título revista: | Discrete and Continuous Dynamical Systems- Series A
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Título revista abreviado: | Discrete Contin. Dyn. Syst. Ser A
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ISSN: | 10780947
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10780947_v36_n12_p6737_DelPezzo |
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Citas:
---------- APA ----------
Del Pezzo, L.M. & Rossi, J.D.
(2016)
. Eigenvalues for a nonlocal pseudo p-Laplacian. Discrete and Continuous Dynamical Systems- Series A, 36(12), 6737-6765.
http://dx.doi.org/10.3934/dcds.2016093---------- CHICAGO ----------
Del Pezzo, L.M., Rossi, J.D.
"Eigenvalues for a nonlocal pseudo p-Laplacian"
. Discrete and Continuous Dynamical Systems- Series A 36, no. 12
(2016) : 6737-6765.
http://dx.doi.org/10.3934/dcds.2016093---------- MLA ----------
Del Pezzo, L.M., Rossi, J.D.
"Eigenvalues for a nonlocal pseudo p-Laplacian"
. Discrete and Continuous Dynamical Systems- Series A, vol. 36, no. 12, 2016, pp. 6737-6765.
http://dx.doi.org/10.3934/dcds.2016093---------- VANCOUVER ----------
Del Pezzo, L.M., Rossi, J.D. Eigenvalues for a nonlocal pseudo p-Laplacian. Discrete Contin. Dyn. Syst. Ser A. 2016;36(12):6737-6765.
http://dx.doi.org/10.3934/dcds.2016093