期刊
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
卷 371, 期 6, 页码 4377-4409出版社
AMER MATHEMATICAL SOC
DOI: 10.1090/tran/7694
关键词
Principal eigenvalue; the Landis conjecture; decay of eigenfunctions; Liouville property
类别
资金
- Army Research Office [W911NF-17-1-001]
- National Science Foundation [DMS-1715210]
- Office of Naval Research [N00014-16-1-2956]
- INSPIRE faculty fellowship [IFA13/MA-32]
- DST-SERB grant [EMR/2016/004810]
- Israel Council for Higher Education
- Israel Science Foundation [970/15]
We present certain Liouville properties of eigenfunctions of second-order elliptic operators with real coefficients, via an approach that is based on stochastic representations of positive solutions, and criticality theory of second-order elliptic operators. These extend results of Y. Pinchover to the case of nonsymmetric operators of Schrodinger type. In particular, we provide an answer to an open problem posed by Pinchover in [Comm. Math. Phys. 272 (2007), pp. 75-84, Problem 5]. In addition, we prove a lower bound on the decay of positive supersolutions of general second-order elliptic operators in any dimension, and discuss its implications to the Landis conjecture.
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