A Sharp Liouville Theorem for Elliptic Operators

2010/02/16 by Priola, Enrico, Wang, Feng-Yu
#35J15 #47D07 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1002.3055

Abstract

We introduce a new condition on elliptic operators L= 1/2\triangle + b ⋅ ∇ which ensures the validity of the Liouville property for bounded solutions to Lu=0 on \R^d. 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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