solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看5402次
On equilibrium shapes of charged flat drops. (arXiv:1607.04920v3 [math.AP] UPDATED)
来源于:arXiv
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. 查看全文>>