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.
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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