We consider a nonlocal isoperimetric problem defined in the whole space RN , whose nonlocal part is given by a Riesz potential with exponent α ⋯ (0,N - 1). We show that critical configurations with positive second variation are local minimizers and satisfy a quantitative inequality with respect to the L1 -norm. This criterion provides the existence of an (explicitly determined) critical threshold determining the interval of volumes for which the ball is a local minimizer, and it allows us to address several global minimality issues.

Local and global minimality results for a nonlocal isoperimetric problem on RN / Bonacini, Marco; Cristoferi, Riccardo. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 2014, 46:4(2014), pp. 2310-2349. [10.1137/130929898]

Local and global minimality results for a nonlocal isoperimetric problem on RN

Bonacini, Marco;
2014-01-01

Abstract

We consider a nonlocal isoperimetric problem defined in the whole space RN , whose nonlocal part is given by a Riesz potential with exponent α ⋯ (0,N - 1). We show that critical configurations with positive second variation are local minimizers and satisfy a quantitative inequality with respect to the L1 -norm. This criterion provides the existence of an (explicitly determined) critical threshold determining the interval of volumes for which the ball is a local minimizer, and it allows us to address several global minimality issues.
2014
4
Bonacini, Marco; Cristoferi, Riccardo
Local and global minimality results for a nonlocal isoperimetric problem on RN / Bonacini, Marco; Cristoferi, Riccardo. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 2014, 46:4(2014), pp. 2310-2349. [10.1137/130929898]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/241363
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