Abstract:
It is proved that, to select a uniqueness class for the magnetic Helmholtz equation, it suffices to impose radiation conditions weaker than the Ikebe–Saito conditions. The self-adjointness of the magnetic Helmholtz operator is proved. The existence of a solution of the inhomogeneous Helmholtz equation satisfying the radiation condition is justified.
Keywords:Helmholtz equation, magnetic Helmholtz operator, self-adjointness, radiation conditions, magnetic Sobolev space, magnetic Hardy inequality, diamagnetic inequality.