Sommerfeld Radiation Condition for Helmholtz equations with long-range potentials
Abstract
We study the electric Helmholtz equation Δu + V u + λu = 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 + pλ 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.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Numerical methods in inverse problems
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Open Access CRIS of the University of Bern
- Publication date
- 1 January 2026
- Language
- EN