Optimal partition problems for the fractional Laplacian

RITORTO, ANTONELLA

ANNALI DI MATEMATICA PURA ED APPLICATA

SPRINGER HEIDELBERG

Año: 2017 p. 1 - 16

0373-3114

In this work, we prove an existence result for an optimal partition problem of the form (Formula presented.)where (Formula presented.) is a cost functional with suitable assumptions of monotonicity and lower semicontinuity, (Formula presented.) is the class of admissible domains and the condition (Formula presented.) is understood in the sense of Gagliardo s-capacity, where (Formula presented.). 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 (Formula presented.), studied in [5].