@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 = {

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.

}, keywords = {Nonlocal isoperimetric problem}, doi = {10.1137/130929898}, url = {http://hdl.handle.net/1963/6984}, author = {Marco Bonacini and Riccardo Cristoferi} }