@article {2013,
	title = {Local and global minimality results for a nonlocal isoperimetric problem on R^N},
	journal = { SIAM Journal on Mathematical Analysis},
	volume = {46},
	number = {Siam journal on mathematical analysis},
	year = {2014},
	pages = {2310-2349},
	publisher = {SIAM Publications},
	abstract = {<p>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.</p>},
	keywords = {Nonlocal isoperimetric problem},
	doi = {10.1137/130929898},
	url = {http://hdl.handle.net/1963/6984},
	author = {Marco Bonacini and Riccardo Cristoferi}
}
