Sommerfeld Radiation Condition for Helmholtz Equations with long-range Potentials

We study the electric Helmholtz equation $\mathrm{\Delta }u+Vu+\lambda u=f$ 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 $\mathrm{\mid }\mathrm{\nabla }K{\mathrm{\mid }}^2=1+\frac{p}{\lambda }$ to improve previous results in that area and extend them to long-range potentials which decay like $\mathrm{\mid }x{\mathrm{\mid }}^{-2-\alpha }$ at infinity, with $\alpha >0$.