A Sharp Liouville Theorem for Elliptic Operators

Details A Sharp Liouville Theorem for Elliptic Operators A Sharp Liouville Theorem for Elliptic Operators

2010-02-16

arxiv.org/abs/1002.3055v1

Mathematics

Analysis of PDEs

Scientific paper

We introduce a new condition on elliptic operators $L= {1/2}\triangle + b
\cdot \nabla $ 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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