A limiting problem for a family of eigenvalue problems involving p-Laplacians

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In this paper we analyse the existence of principal eigenvalues and eigenfunctions for a family of eigenvalue problems described by a system consisting in two partial differential equations involving p-Laplacians. Next, we study the asymptotic behaviour, as p→ ∞, of the sequence of principal eigenfu...

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Autores principales: Mihailescu, M., Rossi, J.D., Stancu-Dumitru, D.
Formato: INPR
Materias:
Distance function
Eigenvalue problem
Viscosity solution
Weak solution
Γ -convergence
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_11391138_v_n_p_Mihailescu
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_11391138_v_n_p_Mihailescu
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spelling todo:paper_11391138_v_n_p_Mihailescu2023-10-03T16:08:01Z A limiting problem for a family of eigenvalue problems involving p-Laplacians Mihailescu, M. Rossi, J.D. Stancu-Dumitru, D. Distance function Eigenvalue problem Viscosity solution Weak solution Γ -convergence In this paper we analyse the existence of principal eigenvalues and eigenfunctions for a family of eigenvalue problems described by a system consisting in two partial differential equations involving p-Laplacians. Next, we study the asymptotic behaviour, as p→ ∞, of the sequence of principal eigenfunctions and we show that, passing eventually to a subsequence, it converges uniformly to a certain limit given by a pair of continuous functions. Moreover, we identify the limiting equations which have as solutions the limiting functions. © 2019, Universidad Complutense de Madrid. INPR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_11391138_v_n_p_Mihailescu
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Distance function
Eigenvalue problem
Viscosity solution
Weak solution
Γ -convergence
spellingShingle Distance function
Eigenvalue problem
Viscosity solution
Weak solution
Γ -convergence
Mihailescu, M.
Rossi, J.D.
Stancu-Dumitru, D.
A limiting problem for a family of eigenvalue problems involving p-Laplacians
topic_facet Distance function
Eigenvalue problem
Viscosity solution
Weak solution
Γ -convergence
description In this paper we analyse the existence of principal eigenvalues and eigenfunctions for a family of eigenvalue problems described by a system consisting in two partial differential equations involving p-Laplacians. Next, we study the asymptotic behaviour, as p→ ∞, of the sequence of principal eigenfunctions and we show that, passing eventually to a subsequence, it converges uniformly to a certain limit given by a pair of continuous functions. Moreover, we identify the limiting equations which have as solutions the limiting functions. © 2019, Universidad Complutense de Madrid.
format INPR
author Mihailescu, M.
Rossi, J.D.
Stancu-Dumitru, D.
author_facet Mihailescu, M.
Rossi, J.D.
Stancu-Dumitru, D.
author_sort Mihailescu, M.
title A limiting problem for a family of eigenvalue problems involving p-Laplacians
title_short A limiting problem for a family of eigenvalue problems involving p-Laplacians
title_full A limiting problem for a family of eigenvalue problems involving p-Laplacians
title_fullStr A limiting problem for a family of eigenvalue problems involving p-Laplacians
title_full_unstemmed A limiting problem for a family of eigenvalue problems involving p-Laplacians
title_sort limiting problem for a family of eigenvalue problems involving p-laplacians
url http://hdl.handle.net/20.500.12110/paper_11391138_v_n_p_Mihailescu
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AT rossijd alimitingproblemforafamilyofeigenvalueproblemsinvolvingplaplacians
AT stancudumitrud alimitingproblemforafamilyofeigenvalueproblemsinvolvingplaplacians
AT mihailescum limitingproblemforafamilyofeigenvalueproblemsinvolvingplaplacians
AT rossijd limitingproblemforafamilyofeigenvalueproblemsinvolvingplaplacians
AT stancudumitrud limitingproblemforafamilyofeigenvalueproblemsinvolvingplaplacians
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