Year: 2025
Type: article
Abstract: We study the electric Helmholtz equation $$\Delta u + Vu + \lambda u =f$$ Δ u + V u + 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 $$|\nabla K|^2=1 + \frac{p}{\lambda }$$ | ∇ K | 2 = 1 + p λ to improve previous results in that area and extend them to long-range potentials which decay like $$|x|^{-2-\alpha }$$ | x | - 2 - α at infinity, with $$\alpha > 0$$ α > 0 .
Author: Eric Ströher
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4415547973