Geodesic
An isoperimetric problem with a Coulombic repulsion and attractive term
ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 14.

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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 B$$ is a local minimizer with respect to any other set with same measure. The global minimality of balls is also addressed.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2018008
Classification : 49Q20
Keywords: Isoperimetric inequality, Coulombic potential

La Manna, Domenico Angelo 1

1 
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La Manna, Domenico Angelo. An isoperimetric problem with a Coulombic repulsion and attractive term. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 14. doi : 10.1051/cocv/2018008. http://geodesic.mathdoc.fr/articles/10.1051/cocv/2018008/

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