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.
An isoperimetric problem with a Coulombic repulsion and attractive term / La Manna, D. A.. - In: ESAIM. COCV. - ISSN 1292-8119. - 25:(2019). [10.1051/cocv/2018008]
An isoperimetric problem with a Coulombic repulsion and attractive term
La Manna D. A.
2019
Abstract
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.File in questo prodotto:
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