{
  "id": "1007.5496",
  "version": "v1",
  "published": "2010-07-30T16:58:34.000Z",
  "updated": "2010-07-30T16:58:34.000Z",
  "title": "BMO solvability and the $A_\\infty$ condition for elliptic operators",
  "authors": [
    "Martin Dindos",
    "Carlos Kenig",
    "Jill Pipher"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish a connection between the absolute continuity of elliptic measure associated to a second order divergence form operator with bounded measurable coefficients with the solvability of an endpoint $BMO$ Dirichlet problem. We show that these two notions are equivalent. As a consequence we obtain an end-point perturbation result, i.e., the solvability of the $BMO$ Dirichlet problem implies $L^p$ solvability for all $p>p_0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-30T16:58:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J25"
    ],
    "keywords": [
      "elliptic operators",
      "bmo solvability",
      "second order divergence form operator",
      "end-point perturbation result",
      "dirichlet problem implies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.5496D"
    }
  }
}