Limiting absorption principle for the electromagnetic Helmholtz equation with singular potentials

Abstract

We study the following Helmholtz equation $$(\nabla +iA(x){)}^{2}u+V_1(x)u+V_2(x)u+\lambda u=f(x)$$ in ${\mathbb{R}}^d$ with magnetic and electric potentials that are singular at the origin and decay at infinity. We prove the existence of a unique solution satisfying a suitable Sommerfeld radiation condition, together with some a priori estimates. We use the limiting absorption method and a multiplier technique of Morawetz type.