Sommerfeld Radiation Condition for Helmholtz Equations with long-range Potentials

We study the electric Helmholtz equation Δ u + Vu + λ u =f and show that, for certain potentials, the solution u given by the limited absorption principle obeys a Sommerfeld radiation condition. We use a non-spherical approach based on the solution K of the eikonal equation |∇ K|²=1 + p/λ to improve previous results in that area and extend them to long-range potentials which decay like |x|-2-α at infinity, with α > 0.