Eigenvalues for a nonlocal pseudo p-Laplacian

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...

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Autores principales: Del Pezzo, L.M., Rossi, J.D.
Formato: JOUR
Materias:
Asymptotic behavior
Dirichlet boundary conditions
Eigenvalues
Nonlocal operator
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_10780947_v36_n12_p6737_DelPezzo
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_10780947_v36_n12_p6737_DelPezzo2023-10-03T16:03:40Z Eigenvalues for a nonlocal pseudo p-Laplacian Del Pezzo, L.M. Rossi, J.D. Asymptotic behavior Dirichlet boundary conditions Eigenvalues Nonlocal operator 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. Fil:Del Pezzo, L.M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10780947_v36_n12_p6737_DelPezzo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Asymptotic behavior
Dirichlet boundary conditions
Eigenvalues
Nonlocal operator
spellingShingle Asymptotic behavior
Dirichlet boundary conditions
Eigenvalues
Nonlocal operator
Del Pezzo, L.M.
Rossi, J.D.
Eigenvalues for a nonlocal pseudo p-Laplacian
topic_facet Asymptotic behavior
Dirichlet boundary conditions
Eigenvalues
Nonlocal operator
description 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.
format JOUR
author Del Pezzo, L.M.
Rossi, J.D.
author_facet Del Pezzo, L.M.
Rossi, J.D.
author_sort Del Pezzo, L.M.
title Eigenvalues for a nonlocal pseudo p-Laplacian
title_short Eigenvalues for a nonlocal pseudo p-Laplacian
title_full Eigenvalues for a nonlocal pseudo p-Laplacian
title_fullStr Eigenvalues for a nonlocal pseudo p-Laplacian
title_full_unstemmed Eigenvalues for a nonlocal pseudo p-Laplacian
title_sort eigenvalues for a nonlocal pseudo p-laplacian
url http://hdl.handle.net/20.500.12110/paper_10780947_v36_n12_p6737_DelPezzo
work_keys_str_mv AT delpezzolm eigenvaluesforanonlocalpseudoplaplacian
AT rossijd eigenvaluesforanonlocalpseudoplaplacian
_version_ 1782029027847962624

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