A sharp Liouville theorem for elliptic operators (Q619703)

Summary: We introduce a new condition on elliptic operators \(L = 1/2 \Delta + b\cdot\nabla \) which ensures the validity of the Liouville property, i.e., all smooth bounded solutions to \(Lu = 0\) on \(\mathbb R^d\) are constant. Such condition is sharp when \(d=1\). We extend our Liouville theorem to more general second order operators in non-divergence form assuming a Cordes type condition.