Conducting Flat Drops in a Confining Potential

Document Type

Article

Publication Date

3-1-2022

Abstract

We study a geometric variational problem arising from modeling two-dimensional charged drops of a perfectly conducting liquid in the presence of an external potential. We characterize the semicontinuous envelope of the energy in terms of a parameter measuring the relative strength of the Coulomb interaction. As a consequence, when the potential is confining and the Coulomb repulsion strength is below a critical value, we show existence and regularity estimates for volume-constrained minimizers. We also derive the Euler–Lagrange equation satisfied by regular critical points, expressing the first variation of the Coulombic energy in terms of the normal 12-derivative of the capacitary potential.

Identifier

85124152208 (Scopus)

Publication Title

Archive for Rational Mechanics and Analysis

External Full Text Location

https://doi.org/10.1007/s00205-021-01738-0

e-ISSN

14320673

ISSN

00039527

First Page

1773

Last Page

1810

Issue

3

Volume

243

Grant

DMS-1614948

Fund Ref

National Science Foundation

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