(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Castro, Agnese di; Novaga, Matteo; Ruffini, Berardo; Valdinoci, Enrico
We characterize the volume-constrained minimizers of a nonlocal free
energy given by the difference of fractional perimeters. Exploiting the
quantitative fractional isoperimetric inequality, we show that balls are the
unique minimizers if the volume is sufficiently small, while the existence
vs. nonexistence of minimizers for large volumes remains open. We also
consider the corresponding isoperimetric problem and prove existence and
regularity of minimizers.
