| Issue |
ESAIM: COCV
Volume 25, 2019
|
|
|---|---|---|
| Article Number | 14 | |
| Number of page(s) | 23 | |
| DOI | https://doi.org/10.1051/cocv/2018008 | |
| Published online | 18 June 2019 | |
An isoperimetric problem with a Coulombic repulsion and attractive term
Universitá degli Studi di Napoli Federico II, Dipartimento di Matematica ed Applicazioni Renato Caccioppoli,
Naples, Italy.
* Corresponding author: domenicolamanna@hotmail.it
Received:
5
October
2017
Accepted:
24
January
2018
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.
Mathematics Subject Classification: 49Q20
Key words: Isoperimetric inequality / Coulombic potential
© EDP Sciences, SMAI 2019
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