Ellipticity of the quantum mechanical Hamiltonians: corner singularity of the helium atom

In paper (Flad and Harutyunyan in Discrete Contin Dyn Syst 420–429, 2011 ) is shown that the Hamiltonian of the helium atom in the Born–Oppenheimer approximation, in the case if two particles coincide, is an edge-degenerate operator, which is elliptic in the corresponding edge calculus. The aim of this paper is an analogous investigation in the case if all three particles coincide. More precisely, we show that the Hamiltonian in the mentioned case is a corner-degenerate operator, which is elliptic as an operator in the corner analysis.