A Sharp Liouville Theorem for Elliptic Operators

Enrico Priola; Feng-Yu Wang

A Sharp Liouville Theorem for Elliptic Operators

Analysis of PDEs 2010-02-17 v1 Probability

Authors: Enrico Priola , Feng-Yu Wang

Abstract

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.

Keywords

liouville theorem operator theory and elliptic operators elliptic partial differential equations

Cite

@article{arxiv.1002.3055,
  title  = {A Sharp Liouville Theorem for Elliptic Operators},
  author = {Enrico Priola and Feng-Yu Wang},
  journal= {arXiv preprint arXiv:1002.3055},
  year   = {2010}
}

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