Conducting Flat Drops in a Confining Potential

Cyrill B. Muratov, Matteo Novaga, Berardo Ruffini

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1773-1810
Number of pages38
JournalArchive for Rational Mechanics and Analysis
Issue number3
StatePublished - Mar 2022

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering


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