Bifurcation and stability for charged drops

In this paper, we investigate the Laplace's equation for the electrical potential of charge drops on exterior domain, and overdetermined boundary conditions are prescribed. We determine the local bifurcation structure with respect to the surface tension coefficient as bifurcation parameter. Furthermore, we establish the stability and the instability near the bifurcation point.

Automated summary

In this paper, we investigate the Laplace's equation for the electrical potential of charge drops on the exterior domain with prescribed overdetermined boundary conditions. We determine the local bifurcation structure with respect to the surface tension coefficient as the bifurcation parameter, and establish the stability and instability near the bifurcation point.