Certain Liouville properties of eigenfunctions of elliptic operators

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dc.contributor.authorArapostathis, Arien_US
dc.contributor.authorBISWAS, ANUPen_US
dc.contributor.authorGANGULY, DEBDIPen_US
dc.contributor.departmentDept. of Mathematicsen_US
dc.date.accessioned2019-09-09T11:38:48Z
dc.date.available2019-09-09T11:38:48Z
dc.date.issued2019-03en_US
dc.description.abstractWe 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 Schrödinger 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.en_US
dc.identifier.citationTransaction of the American Mathematical Society, 371 (6), 4377-4409 .en_US
dc.identifier.issn1088-6850en_US
dc.identifier.issn0002-9947en_US
dc.identifier.sourcetitleTransaction of the American Mathematical Societyen_US
dc.identifier.urihttp://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/4028
dc.identifier.urihttps://doi.org/10.1090/tran/7694
dc.language.isoenen_US
dc.publication.originofpublisherForeignen_US
dc.publisherAmerican Mathematical Societyen_US
dc.subjectCertain Liouvilleen_US
dc.subjectProperties of eigenfunctionsen_US
dc.subjectElliptic operatorsen_US
dc.subjectDiscuss its implicationsen_US
dc.subject2019en_US
dc.titleCertain Liouville properties of eigenfunctions of elliptic operatorsen_US
dc.typeArticleen_US

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