Optimal partition problems for the fractional Laplacian

In this work, we prove an existence result for an optimal partition problem of the form min{Fs(A1, …, Am) : Ai ∈ As, Ai ∩ Aj = ∅ for i ≠ j}, where Fs is a cost functional with suitable assumptions of monotonicity and lower semicontinuity, As is the class of admissible domains and the condition Ai∩ A...

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Autor principal: Ritorto, A.
Formato: JOUR
Materias:
Fractional capacities
Fractional partial equations
Optimal partition
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03733114_v197_n2_p501_Ritorto
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_03733114_v197_n2_p501_Ritorto2023-10-03T15:30:20Z Optimal partition problems for the fractional Laplacian Ritorto, A. Fractional capacities Fractional partial equations Optimal partition In this work, we prove an existence result for an optimal partition problem of the form min{Fs(A1, …, Am) : Ai ∈ As, Ai ∩ Aj = ∅ for i ≠ j}, where Fs is a cost functional with suitable assumptions of monotonicity and lower semicontinuity, As is the class of admissible domains and the condition Ai∩ Aj= ∅ is understood in the sense of Gagliardo s-capacity, where 0 < s < 1. Examples of this type of problem are related to fractional eigenvalues. As the main outcome of this article, we prove some type of convergence of the s-minimizers to the minimizer of the problem with s= 1 , studied in [5]. © 2017, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03733114_v197_n2_p501_Ritorto
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Fractional capacities
Fractional partial equations
Optimal partition
spellingShingle Fractional capacities
Fractional partial equations
Optimal partition
Ritorto, A.
Optimal partition problems for the fractional Laplacian
topic_facet Fractional capacities
Fractional partial equations
Optimal partition
description In this work, we prove an existence result for an optimal partition problem of the form min{Fs(A1, …, Am) : Ai ∈ As, Ai ∩ Aj = ∅ for i ≠ j}, where Fs is a cost functional with suitable assumptions of monotonicity and lower semicontinuity, As is the class of admissible domains and the condition Ai∩ Aj= ∅ is understood in the sense of Gagliardo s-capacity, where 0 < s < 1. Examples of this type of problem are related to fractional eigenvalues. As the main outcome of this article, we prove some type of convergence of the s-minimizers to the minimizer of the problem with s= 1 , studied in [5]. © 2017, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany.
format JOUR
author Ritorto, A.
author_facet Ritorto, A.
author_sort Ritorto, A.
title Optimal partition problems for the fractional Laplacian
title_short Optimal partition problems for the fractional Laplacian
title_full Optimal partition problems for the fractional Laplacian
title_fullStr Optimal partition problems for the fractional Laplacian
title_full_unstemmed Optimal partition problems for the fractional Laplacian
title_sort optimal partition problems for the fractional laplacian
url http://hdl.handle.net/20.500.12110/paper_03733114_v197_n2_p501_Ritorto
work_keys_str_mv AT ritortoa optimalpartitionproblemsforthefractionallaplacian
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