Sommerfeld Radiation Condition for Helmholtz Equations with long-range Potentials

2024/02/19 by Ströher, Eric
#35B25 (Primary) 35J05 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.12306

Abstract

We study the electric Helmholtz equation Δu + Vu + 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 + \fracpλ 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.

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