Artículos de revistas
Optimal partition problems for the fractional Laplacian
Fecha
2018-04Registro en:
Ritorto, Antonella; Optimal partition problems for the fractional Laplacian; Springer Heidelberg; Annali Di Matematica Pura Ed Applicata; 197; 2; 4-2018; 501-516
0373-3114
CONICET Digital
CONICET
Autor
Ritorto, Antonella
Resumen
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].