A Liouville-Type Theorem for Harmonic Functions on Exterior Domains

Liouville’s classical theorem assures that every harmonic function on the whole space Rn that is moreover bounded from below is a constant. It is easy to observe that, generally, the same result does not hold if we replace the whole space Rn with an exterior domain. Hence, in this paper we provide a Liouville-type theorem for harmonic functions defined on exterior domains