{
  "id": "1511.03188",
  "version": "v1",
  "published": "2015-11-10T17:10:18.000Z",
  "updated": "2015-11-10T17:10:18.000Z",
  "title": "Pointwise estimates of solutions to semilinear elliptic equations and inequalities",
  "authors": [
    "Alexander Grigor'yan",
    "Igor Verbitsky"
  ],
  "comment": "32 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "We obtain sharp pointwise estimates for positive solutions to the equation $-Lu+Vu^q=f$, where $L$ is an elliptic operator in divergence form, $q\\in\\mathbb{R}\\setminus \\{0\\}$, $f\\geq 0$ and $V$ is a function that may change sign, in a domain $\\Omega$ in $\\mathbb{R}^{n}$, or in a weighted Riemannian manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-10T17:10:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J61",
      "58J05"
    ],
    "keywords": [
      "semilinear elliptic equations",
      "inequalities",
      "sharp pointwise estimates",
      "weighted riemannian manifold",
      "elliptic operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151103188G"
    }
  }
}