The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians

In this paper, we study the behavior as p→ ∞ of eigenvalues and eigenfunctions of a system of p-Laplacians, that is (Formula presented.) in a bounded smooth domain Ω. Here α+ β= p. We assume that α/p→Γ and β/p→1-Γ as p→ ∞ and we prove that for the first eigenvalue λ1,p we have (λ1,p)1/p→λ∞=1/maxx∈Ωd...

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Autores principales:	Bonheure, D., Rossi, J.D., Saintier, N.
Formato:	JOUR
Materias:	Infinity Laplacian Nonlinear eigenvalue problem p-Laplacian Viscosity solutions
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_03733114_v195_n5_p1771_Bonheure
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_03733114_v195_n5_p1771_Bonheure2023-10-03T15:30:19Z The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians Bonheure, D. Rossi, J.D. Saintier, N. Infinity Laplacian Nonlinear eigenvalue problem p-Laplacian Viscosity solutions In this paper, we study the behavior as p→ ∞ of eigenvalues and eigenfunctions of a system of p-Laplacians, that is (Formula presented.) in a bounded smooth domain Ω. Here α+ β= p. We assume that α/p→Γ and β/p→1-Γ as p→ ∞ and we prove that for the first eigenvalue λ1,p we have (λ1,p)1/p→λ∞=1/maxx∈Ωdist(x,∂Ω).Concerning the eigenfunctions (up, vp) associated with λ1,p normalized by ∫Ω\|up\|α\|vp\|β=1, there is a uniform limit (u∞, v∞) that is a solution to a limit minimization problem as well as a viscosity solution to (Formula presented.) In addition, we also analyze the limit PDE when we consider higher eigenvalues. © 2015, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg. 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_03733114_v195_n5_p1771_Bonheure
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Infinity Laplacian Nonlinear eigenvalue problem p-Laplacian Viscosity solutions
spellingShingle	Infinity Laplacian Nonlinear eigenvalue problem p-Laplacian Viscosity solutions Bonheure, D. Rossi, J.D. Saintier, N. The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
topic_facet	Infinity Laplacian Nonlinear eigenvalue problem p-Laplacian Viscosity solutions
description	In this paper, we study the behavior as p→ ∞ of eigenvalues and eigenfunctions of a system of p-Laplacians, that is (Formula presented.) in a bounded smooth domain Ω. Here α+ β= p. We assume that α/p→Γ and β/p→1-Γ as p→ ∞ and we prove that for the first eigenvalue λ1,p we have (λ1,p)1/p→λ∞=1/maxx∈Ωdist(x,∂Ω).Concerning the eigenfunctions (up, vp) associated with λ1,p normalized by ∫Ω\|up\|α\|vp\|β=1, there is a uniform limit (u∞, v∞) that is a solution to a limit minimization problem as well as a viscosity solution to (Formula presented.) In addition, we also analyze the limit PDE when we consider higher eigenvalues. © 2015, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg.
format	JOUR
author	Bonheure, D. Rossi, J.D. Saintier, N.
author_facet	Bonheure, D. Rossi, J.D. Saintier, N.
author_sort	Bonheure, D.
title	The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
title_short	The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
title_full	The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
title_fullStr	The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
title_full_unstemmed	The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians
title_sort	limit as p→ ∞ in the eigenvalue problem for a system of p-laplacians
url	http://hdl.handle.net/20.500.12110/paper_03733114_v195_n5_p1771_Bonheure
work_keys_str_mv	AT bonheured thelimitaspintheeigenvalueproblemforasystemofplaplacians AT rossijd thelimitaspintheeigenvalueproblemforasystemofplaplacians AT saintiern thelimitaspintheeigenvalueproblemforasystemofplaplacians AT bonheured limitaspintheeigenvalueproblemforasystemofplaplacians AT rossijd limitaspintheeigenvalueproblemforasystemofplaplacians AT saintiern limitaspintheeigenvalueproblemforasystemofplaplacians
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The limit as p→ ∞ in the eigenvalue problem for a system of p-Laplacians

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