Optimal partition problems for the fractional Laplacian

RITORTO, ANTONELLA

Seminario; Seminar, Universidad Autónoma de Madrid; 2018

In this work, we prove an existence result for an optimal partitionproblem where the cost functional has suitable assumptions of monotonicity andlower semicontinuity. As is the class of admissible domains and the condition of being disjointed 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 themain 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 Existenceresults for some optimal partition problems, Dorin Bucur, Giuseppe Buttazzo,and Antoine Henrot,, Adv. Math. Sci. Appl. 8 (1998), no. 2, 571579. MR1657219.