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. © 2017 Wiley Periodicals, Inc.
Muratov C, Novaga N, Ruffini B (2018). On equilibrium shapes of charged flat drops. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 71, 1049-1073 [10.1002/cpa.21739].
On equilibrium shapes of charged flat drops
Ruffini B
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. © 2017 Wiley Periodicals, Inc.File | Dimensione | Formato | |
---|---|---|---|
murnovruf.pdf
accesso aperto
Tipo:
Postprint
Licenza:
Licenza per accesso libero gratuito
Dimensione
1.19 MB
Formato
Adobe PDF
|
1.19 MB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.