Limiting absorption principle for the electromagnetic Helmholtz equation with singular potentials

We study the following Helmholtz equation $(\nabla +iA(x))^{2} u+ V_{1}(x) u + V_{2}(x) u + λu = f(x)$ 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.

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