Lp-Liouville Property for Non-Local Operators
Analysis of PDEs
2025-01-17 v1 Probability
Abstract
The Lp-Liouville property of a non-local operator A is investigated via the associated Dirichlet form. We will show that any non-negative continuous Lp E-subharmonic functions are constant under a quite mild assumption on the kernel of E if p is not less than 2. On the contrary, if 1 < p < 2, we need an additional assumption: either, the kernel has compact support; or f is Holder continuous.
Keywords
Cite
@article{arxiv.1103.1781,
title = {Lp-Liouville Property for Non-Local Operators},
author = {Jun Masamune and Toshihiro Uemura},
journal= {arXiv preprint arXiv:1103.1781},
year = {2025}
}
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22 pages, 0 figures