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On minimizers of an
isoperimetric problem with long-range interactions under a
convexity constraint
Michael Goldman, Matteo Novaga and Berardo Ruffini |
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Vol. 11 (2018), No. 5, 1113–1142
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Abstract |
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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 -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. |
Keywords
nonlocal isoperimetric problem, convexity constraint
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Mathematical Subject Classification 2010
Primary: 49J30, 49J45, 49S05
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Milestones
Received: 8 November 2016
Revised: 6 July 2017
Accepted: 2 January 2018
Published: 11 April 2018
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Authors |
| Michael Goldman | |
| Université Paris-Diderot Sorbonne Paris-Cité Sorbonne Université, CNRS Laboratoire Jacques-Louis Lions Paris France |
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| Matteo Novaga | |
| Dipartimento di Matematica Università di Pisa Pisa Italy |
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| Berardo Ruffini | |
| Institut Montpelliérain Alexander
Grothendieck University of Montpellier, CNRS Montpellier France |
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