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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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03733114_v197_n2_p501_Ritorto |
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| Sumario: | 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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