On Equilibrium Shape of Charged Flat Drops

Cyrill B. Muratov, Matteo Novaga, Berardo Ruffini

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1049-1073
Number of pages25
JournalCommunications on Pure and Applied Mathematics
Issue number6
StatePublished - Jun 2018

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


Dive into the research topics of 'On Equilibrium Shape of Charged Flat Drops'. Together they form a unique fingerprint.

Cite this