Limiting absorption principle for the electromagnetic Helmholtz equation with singular potentials

摘要

We study the following Helmholtz equation $$ (abla +iA(x))^{2} u+ V_{1}(x)u + V_{2}(x) u + lambda u = f(x) $$ in $mathbb{R}^d$ with magnetic andelectric potentials that are singular at the origin and decay at infinity. Weprove the existence of a unique solution satisfying a suitable Sommerfeldradiation condition, together with some a priori estimates. We use the limitingabsorption method and a multiplier technique of Morawetz type.