Analysis & PDE

  • Anal. PDE
  • Volume 11, Number 5 (2018), 1113-1142.

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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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.

Article information

Source
Anal. PDE, Volume 11, Number 5 (2018), 1113-1142.

Dates
Received: 8 November 2016
Revised: 6 July 2017
Accepted: 2 January 2018
First available in Project Euclid: 17 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.apde/1523930416

Digital Object Identifier
doi:10.2140/apde.2018.11.1113

Mathematical Reviews number (MathSciNet)
MR3785601

Zentralblatt MATH identifier
06866544

Subjects
Primary: 49J30: Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 49J45: Methods involving semicontinuity and convergence; relaxation 49S05: Variational principles of physics (should also be assigned at least one other classification number in section 49)

Keywords
nonlocal isoperimetric problem convexity constraint

Citation

Goldman, Michael; Novaga, Matteo; Ruffini, Berardo. On minimizers of an isoperimetric problem with long-range interactions under a convexity constraint. Anal. PDE 11 (2018), no. 5, 1113--1142. doi:10.2140/apde.2018.11.1113. https://projecteuclid.org/euclid.apde/1523930416


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