Lp-Liouville Property for Non-Local Operators

Details Lp-Liouville Property for Non-Local Operators Lp-Liouville Property for Non-Local Operators

2011-03-09

arxiv.org/abs/1103.1781v1

Mathematics

Analysis of PDEs

22 pages, 0 figures

Scientific paper

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.

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