On Equilibrium Shape of Charged Flat Drops

Document Type

Article

Publication Date

6-1-2018

Abstract

The equilibrium shapes of two-dimensional charged, perfectly conducting liquid drops are governed by a geometric variational problem that involves a perimeter term modeling line tension and a capacitary term modeling Coulombic repulsion. Here we give a complete explicit solution to this variational problem. Namely, we show that at fixed total charge a ball of a particular radius is the unique global minimizer among all sufficiently regular sets in the plane. For sets whose area is also fixed, we show that balls are the only minimizers if the charge is less than or equal to a critical charge, while for larger charge minimizers do not exist. Analogous results hold for drops whose potential, rather than charge, is fixed. © 2018 Wiley Periodicals, Inc.

Identifier

85041234485 (Scopus)

Publication Title

Communications on Pure and Applied Mathematics

External Full Text Location

https://doi.org/10.1002/cpa.21739

e-ISSN

10970312

ISSN

00103640

First Page

1049

Last Page

1073

Issue

6

Volume

71

Grant

DMS-1313687

Fund Ref

National Science Foundation

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