A nonlocal optimal partition problem

RITORTO, ANTONELLA

Ciudad Autónoma de Buenos Aires

Simposio; V International Symposium on Nonlinear Equations and Free Boundary Problems In honor of Prof. Noemi Wolanski; 2017

We prove an existence result for an optimal partition problem where the cost function has suitable assumptions of monotonicity andlower semicontinuity. As is the class of admissible domains and the conditionbeing 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. We alsodemonstrate some type of convergence of the s-minimizers to the minimizer ofthe problem with s = 1, studied in Existence results for some optimal partitionproblems, Bucur-Buttazzo-Henrot, 1998.