global minimality
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An isoperimetric problem with a Coulombic repulsion and attractive term

2019 ◽  
Vol 25 ◽  
pp. 14
Author(s):  
Domenico Angelo La Manna
Keyword(s):  
Point Charge ◽  
Isoperimetric Problem ◽  
Coulomb Repulsion ◽  
Local Minimizer ◽  
Coulombic Repulsion ◽  
Global Minimality ◽  
Optimal Radius

We study an energy given by the sum of the perimeter of a set, a Coulomb repulsion term of the set with itself and an attraction term of the set to a point charge. We prove that there exists an optimal radius r0 such that if r < r0 the ball Br is a local minimizer with respect to any other set with same measure. The global minimality of balls is also addressed.

scholarly journals Local and global minimality issues for a nonlocal isoperimetric problem on $\mathbb R^N$

2016 ◽  
Vol 27 (1) ◽  
pp. 37-50
Author(s):  
Marco Bonacini ◽  
Riccardo Cristoferi
Keyword(s):  
Isoperimetric Problem ◽  
Global Minimality

scholarly journals Local and Global Minimality Results for a Nonlocal Isoperimetric Problem on $\mathbb{R}^N$

2014 ◽  
Vol 46 (4) ◽  
pp. 2310-2349 ◽  
Author(s):  
M. Bonacini ◽  
R. Cristoferi
Keyword(s):  
Isoperimetric Problem ◽  
Global Minimality
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