On minimizers of an isoperimetric problem with long-range interactions under a convexity constraint

Michael Goldman; Matteo Novaga; Berardo Ruffini

doi:10.2140/apde.2018.11.1113

On minimizers of an isoperimetric problem with long-range interactions under a convexity constraint

Michael Goldman, Matteo Novaga, Berardo Ruffini

Research output: Contribution to journal › Article › peer-review

Abstract

We study a variational problem modeling the behavior at equilibrium of charged liquid drops under a convexity constraint. After proving the well-posedness of the model, we show C^1,1-regularity of minimizers for the Coulombic interaction in dimension two. As a by-product we obtain that balls are the unique minimizers for small charge. Eventually, we study the asymptotic behavior of minimizers, as the charge goes to infinity.

Original language	English
Pages (from-to)	1113-1142
Number of pages	30
Journal	Analysis and PDE
Volume	11
Issue number	5
DOIs	https://doi.org/10.2140/apde.2018.11.1113
Publication status	Published - 1 Jan 2018
Externally published	Yes

Keywords

Convexity constraint
Nonlocal isoperimetric problem

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10.2140/apde.2018.11.1113

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title = "On minimizers of an isoperimetric problem with long-range interactions under a convexity constraint",

abstract = "We study a variational problem modeling the behavior at equilibrium of charged liquid drops under a convexity constraint. After proving the well-posedness of the model, we show C1,1-regularity of minimizers for the Coulombic interaction in dimension two. As a by-product we obtain that balls are the unique minimizers for small charge. Eventually, we study the asymptotic behavior of minimizers, as the charge goes to infinity.",

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AB - We study a variational problem modeling the behavior at equilibrium of charged liquid drops under a convexity constraint. After proving the well-posedness of the model, we show C1,1-regularity of minimizers for the Coulombic interaction in dimension two. As a by-product we obtain that balls are the unique minimizers for small charge. Eventually, we study the asymptotic behavior of minimizers, as the charge goes to infinity.

KW - Convexity constraint

KW - Nonlocal isoperimetric problem

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DO - 10.2140/apde.2018.11.1113

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JO - Analysis and PDE

JF - Analysis and PDE

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On minimizers of an isoperimetric problem with long-range interactions under a convexity constraint

Abstract

Keywords

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