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Abstract:

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.

Registro:

Documento: Artículo
Título:Optimal partition problems for the fractional Laplacian
Autor:Ritorto, A.
Filiación:Departamento de Matemática, FCEN – Universidad de Buenos Aires and IMAS – CONICET, Buenos Aires, Argentina
Palabras clave:Fractional capacities; Fractional partial equations; Optimal partition
Año:2018
Volumen:197
Número:2
Página de inicio:501
Página de fin:516
DOI: http://dx.doi.org/10.1007/s10231-017-0689-5
Título revista:Annali di Matematica Pura ed Applicata
Título revista abreviado:Ann. Mat. Pura Appl.
ISSN:03733114
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v197_n2_p501_Ritorto

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Citas:

---------- APA ----------
(2018) . Optimal partition problems for the fractional Laplacian. Annali di Matematica Pura ed Applicata, 197(2), 501-516.
http://dx.doi.org/10.1007/s10231-017-0689-5
---------- CHICAGO ----------
Ritorto, A. "Optimal partition problems for the fractional Laplacian" . Annali di Matematica Pura ed Applicata 197, no. 2 (2018) : 501-516.
http://dx.doi.org/10.1007/s10231-017-0689-5
---------- MLA ----------
Ritorto, A. "Optimal partition problems for the fractional Laplacian" . Annali di Matematica Pura ed Applicata, vol. 197, no. 2, 2018, pp. 501-516.
http://dx.doi.org/10.1007/s10231-017-0689-5
---------- VANCOUVER ----------
Ritorto, A. Optimal partition problems for the fractional Laplacian. Ann. Mat. Pura Appl. 2018;197(2):501-516.
http://dx.doi.org/10.1007/s10231-017-0689-5