{
  "id": "2302.01211",
  "version": "v1",
  "published": "2023-02-02T16:45:36.000Z",
  "updated": "2023-02-02T16:45:36.000Z",
  "title": "On weak solutions to linear elliptic equations with $L^2$-drifts of negative divergence",
  "authors": [
    "Haesung Lee"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show the existence and uniqueness as well as boundedness of weak solutions to linear elliptic equations with $L^2$-drifts of negative divergence and singular zero-order terms which are positive. In particular, using Dirichlet form theory we connect a unique solution to the corresponding resolvent and obtain the $L^r$-contraction properties of the unique solution. Furthermore, an elliptic $L^1$-stability is derived through the $L^1$-contraction property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-02T16:45:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J15",
      "35J25",
      "31C25",
      "35B35"
    ],
    "keywords": [
      "linear elliptic equations",
      "weak solutions",
      "negative divergence",
      "contraction property",
      "unique solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}