01060nas a2200157 4500008004100000245008400041210006900125260002200194300001400216490000700230520054900237653003500786100002000821700002500841856003600866 2014 en d00aLocal and global minimality results for a nonlocal isoperimetric problem on R^N0 aLocal and global minimality results for a nonlocal isoperimetric bSIAM Publications a2310-23490 v463 a
We consider a nonlocal isoperimetric problem defined in the whole space R^N, whose nonlocal part is given by a Riesz potential with exponent $\alpha\in(0, N-1)$. We show that critical configurations with positive second variation are local minimizers and satisfy a quantitative inequality with respect to the L^1-norm. This criterion provides the existence of a (explicitly determined) critical threshold determining the interval of volumes for which the ball is a local minimizer, and allows to address several global minimality issues.
10aNonlocal isoperimetric problem1 aBonacini, Marco1 aCristoferi, Riccardo uhttp://hdl.handle.net/1963/6984