The Morse property for functions of Kirchhoff-routh path type

For a bounded domain Ω ⊂ Rn let HΩ : Ω ×Ω → R be the regular part of the Dirichlet Green function for the Laplace operator. Given a fixed arbitrary C2 function f : D → R, defined on an open subset D ⊂ RnN, and fixed coefficients λ1, . . ., λN ∈ R{0} we consider the function fΩ: D∩ΩN → R defined as N (formula presented). j,k=1 We prove that fΩ is a Morse function for most domains Ω of class Cm+2,α, any m ≥ 0, 0 < α < 1. This applies in particular to the Robin function h : Ω → R, h(x) = HΩ(x, x), and to the Kirchhoff-Routh path function where Ω ⊂ R2, D = {x ∈ R2N : xj 6= xk for j 6= k}, and (formula presented).