Bifurcation of the equivariant minimal interfaces in a hydromechanics problem (Q1809777)

A variational bifurcation problem about the capillary interface of two fluids with densities \(\rho_1\), \(\rho_2\), \(\rho_2-\rho_1 >0\) in a cylinder with a section \(\Omega\subset \mathbb{R}^2\), \(w_{\mid{\partial\Omega}}=0\), is considered. The case of 2-dimensional kernel of the linearized operator is investigated.