{
  "id": "1408.7111",
  "version": "v1",
  "published": "2014-08-29T19:36:47.000Z",
  "updated": "2014-08-29T19:36:47.000Z",
  "title": "Local behavior of solutions of the stationary Schr\\\" odinger equation with singular potentials and bounds on the density of states of Schrödinger operators",
  "authors": [
    "Abel Klein",
    "C. S. Sidney Tsang"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the local behavior of solutions of the stationary Schr\\\" od\\-inger equation with singular potentials, establishing a local decomposition into a homogeneous harmonic polynomial and a lower order term. Combining a corollary to this result with a quantitative unique continuation principle for singular potentials we obtain log-H\\\"older continuity for the density of states outer-measure in one, two, and three dimensions for Schr\\\" odinger operators with singular potentials, results that hold for the density of states measure when it exists.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-29T19:36:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B99",
      "81Q10"
    ],
    "keywords": [
      "singular potentials",
      "local behavior",
      "odinger equation",
      "schrödinger operators",
      "stationary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.7111K"
    }
  }
}