Browsing by Author "Ruffini, Berardo"

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    Nonlocal isoperimetric problems
    (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.