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Search: MSC category 31C05 ( Harmonic, subharmonic, superharmonic functions )

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1. CJM 1998 (vol 50 pp. 487)

Barlow, Martin T.
On the Liouville property for divergence form operators
In this paper we construct a bounded strictly positive function $\sigma$ such that the Liouville property fails for the divergence form operator $L=\nabla (\sigma^2 \nabla)$. Since in addition $\Delta \sigma/\sigma$ is bounded, this example also gives a negative answer to a problem of Berestycki, Caffarelli and Nirenberg concerning linear Schr\"odinger operators.

Categories:31C05, 60H10, 35J10

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