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arXiv · 1307.5269

Local and global minimality results for a nonlocal isoperimetric problem on R^N

Marco Bonacini·Riccardo Cristoferi
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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.

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Marco Bonacini, Riccardo Cristoferi. 2013-07-19. Local and global minimality results for a nonlocal isoperimetric problem on R^N. https://doi.org/10.1137/130929898

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