{
  "id": "1708.09640",
  "version": "v1",
  "published": "2017-08-31T09:47:40.000Z",
  "updated": "2017-08-31T09:47:40.000Z",
  "title": "Some Liouville-type results for eigenfunctions of elliptic operators",
  "authors": [
    "Ari Arapostathis",
    "Anup Biswas",
    "Debdip Ganguly"
  ],
  "comment": "28 pages",
  "categories": [
    "math.FA",
    "math.AP",
    "math.PR"
  ],
  "abstract": "This article has two objectives. First, we present some Liouville-type results for eigenfunctions of second-order elliptic operators with real coefficients. We extend results of Y. Pinchover [$Comm.\\ Math.\\ Phys.$ 272 (2007), pp. 75-84] to the case of $nonsymmetric$ operators of Schr\\\"odinger type. In particular, we provide an answer to an open problem posed by Pinchover in [$Comm.\\ Math.\\ Phys.$ 272 (2007), Problem 5]. Second, 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. Our approach is based on stochastic representations of positive solutions, and criticality theory of second-order elliptic operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-31T09:47:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J15",
      "35A02",
      "35B40",
      "35B60"
    ],
    "keywords": [
      "liouville-type results",
      "eigenfunctions",
      "general second-order elliptic operators",
      "stochastic representations",
      "landis conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}