{
  "id": "1008.3873",
  "version": "v3",
  "published": "2010-08-23T17:56:56.000Z",
  "updated": "2012-10-11T06:17:15.000Z",
  "title": "Isolated singularities of positive solutions of p-Laplacian type equations in R^d",
  "authors": [
    "Martin Fraas",
    "Yehuda Pinchover"
  ],
  "comment": "26 pages, minor corrections, published version",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the behavior of positive solutions of p-Laplacian type elliptic equations of the form Q'(u) := -p-Laplacian(u) + V |u|^(p-2) u = 0 in Omega near an isolated singular point zeta, where 1 < p < inf, Omega is a domain in R^d with d > 1, and zeta = 0 or zeta = inf. We obtain removable singularity theorems for positive solutions near zeta. In particular, using a new three-spheres theorems for certain solutions of the above equation near zeta we prove that if V belongs to a certain Kato class near zeta and p>d (respectively, p<d), then any positive solution u of the equation Q'(u)=0 in a punctured neighborhood of zeta=0 (respectively, zeta=inf) is in fact continuous at zeta. Under further assumptions we find the asymptotic behavior of u near zeta.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-10-11T06:17:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35B09",
      "35B53",
      "35J92"
    ],
    "keywords": [
      "positive solution",
      "p-laplacian type equations",
      "isolated singularities",
      "singularity",
      "p-laplacian type elliptic equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.3873F"
    }
  }
}