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arXiv · 2001.02528

A Liouville theorem for Lévy generators

Franziska Kühn
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Abstract

Under mild assumptions, we establish a Liouville theorem for the "Laplace" equation $Au=0$ associated with the infinitesimal generator $A$ of a Lévy process: If $u$ is a weak solution to $Au=0$ which is at most of (suitable) polynomial growth, then $u$ is a polynomial. As a by-product, we obtain new regularity estimates for semigroups associated with Lévy processes.

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Franziska Kühn. 2020-11-21. A Liouville theorem for Lévy generators. https://doi.org/10.1007/s11117-020-00800-7

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