Non-spherical equilibrium shapes in the liquid drop model
Mathematical Physics
2019-09-04 v2 Analysis of PDEs
math.MP
Abstract
We prove the existence of a family of volume-constrained critical points of the liquid drop functional, which are cylindrically but not spherically symmetric. This family bifurcates from the ball and exchanges stability with it.
Cite
@article{arxiv.1903.04344,
title = {Non-spherical equilibrium shapes in the liquid drop model},
author = {Rupert L. Frank},
journal= {arXiv preprint arXiv:1903.04344},
year = {2019}
}
Comments
25 pages; contribution to the proceedings of the ICMP 2018; second version contains more precise energy asymptotics (new Theorem 6)