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
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.
Anal. PDE, Volume 11, Number 5 (2018), 1113-1142.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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)
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