%0 Journal Article %J SIAM Journal on Mathematical Analysis %D 2014 %T Local and global minimality results for a nonlocal isoperimetric problem on R^N %A Marco Bonacini %A Riccardo Cristoferi %K Nonlocal isoperimetric problem %X

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.

%B SIAM Journal on Mathematical Analysis %I SIAM Publications %V 46 %P 2310-2349 %G en %U http://hdl.handle.net/1963/6984 %N 4 %1 6976 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Marco Bonacini (mbonacin@sissa.it) on 2013-07-19T15:56:58Z No. of bitstreams: 1 boncri_fin.pdf: 567997 bytes, checksum: a24d4e9e6bbd6f176558b4d007dba6e3 (MD5) %R 10.1137/130929898