Abstract

We introduce a new condition on elliptic operators L = 1/2 Δ + b∙ ∇ which ensures the validity of the Liouville property, i.e., all smooth bounded solutions to Lu = 0 on 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.

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