A sharp Liouville theorem for elliptic operators
Enrico Priola
Università di Torino, ItalyFeng-Yu Wang
Swansea University, Singleton Park, UK
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Abstract
We introduce a new condition on elliptic operators which ensures the validity of the Liouville property, i.e., all smooth bounded solutions to on are constant. Such condition is sharp when . We extend our Liouville theorem to more general second order operators in non-divergence form assuming a Cordes type condition.
Cite this article
Enrico Priola, Feng-Yu Wang, A sharp Liouville theorem for elliptic operators. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 21 (2010), no. 4, pp. 441–445
DOI 10.4171/RLM/582